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# Directional Derivative : IIT JAM 2018 Problem 42 # Understand the problem

[/et_pb_text][et_pb_text _builder_version="4.1" text_font="Raleway||||||||" background_color="#f4f4f4" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px" box_shadow_style="preset2"]Let for Then the absolute value of the directional derivative of in the direction of the line , at the point is _____

[/et_pb_code][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="4.1" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="4.1"]IIT JAM 2018[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="4.1" open="off"]Directional Derivative [/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.1" open="off"]Easy[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.1" open="off"]

Generalized Directional Derivatives  By Pastor Karel

[/et_pb_text][et_pb_tabs active_tab_background_color="#0c71c3" inactive_tab_background_color="#000000" _builder_version="4.1" tab_text_color="#ffffff" tab_font="||||||||" background_color="#ffffff" hover_enabled="0"][et_pb_tab title="Hint 0" _builder_version="3.22.4"]Do you really need a hint? Try it first!

[/et_pb_tab][et_pb_tab title="Hint 1" _builder_version="4.1" hover_enabled="0"] The rate of change of in the direction of the unit vector is called the directional derivative and is denoted by . The defination of directional derivative is . Here if you consider to be and then we will get to be , and respectively. If you observe closely, this is nothing but differentiating the function w.r.t and keeping all the other thing constant.

Now by the above definition can you try to solve the problem ???????

[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="4.1"]

The points on the straight line  So any point on the straight line would be of the form Here the direction of the straight line would be Now we have to consider the unit vector in that direction and so the unit vector would be Here the absolute value of the directional derivative would be . Would you like to calculate this dot product?

[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="4.1"] i.e the co-ordinates involving partial derivative of . So, Then (Ans) .

# Similar Problems

[/et_pb_text][et_pb_post_slider include_categories="12" image_placement="left" _builder_version="4.1"][/et_pb_post_slider][et_pb_divider _builder_version="3.22.4" background_color="#0c71c3"][/et_pb_divider][/et_pb_column][/et_pb_row][/et_pb_section]

# Understand the problem

[/et_pb_text][et_pb_text _builder_version="4.1" text_font="Raleway||||||||" background_color="#f4f4f4" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px" box_shadow_style="preset2"]Let for Then the absolute value of the directional derivative of in the direction of the line , at the point is _____

[/et_pb_code][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="4.1" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="4.1"]IIT JAM 2018[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="4.1" open="off"]Directional Derivative [/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.1" open="off"]Easy[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.1" open="off"]

Generalized Directional Derivatives  By Pastor Karel

[/et_pb_text][et_pb_tabs active_tab_background_color="#0c71c3" inactive_tab_background_color="#000000" _builder_version="4.1" tab_text_color="#ffffff" tab_font="||||||||" background_color="#ffffff" hover_enabled="0"][et_pb_tab title="Hint 0" _builder_version="3.22.4"]Do you really need a hint? Try it first!

[/et_pb_tab][et_pb_tab title="Hint 1" _builder_version="4.1" hover_enabled="0"] The rate of change of in the direction of the unit vector is called the directional derivative and is denoted by . The defination of directional derivative is . Here if you consider to be and then we will get to be , and respectively. If you observe closely, this is nothing but differentiating the function w.r.t and keeping all the other thing constant.

Now by the above definition can you try to solve the problem ???????

[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="4.1"]

The points on the straight line  So any point on the straight line would be of the form Here the direction of the straight line would be Now we have to consider the unit vector in that direction and so the unit vector would be Here the absolute value of the directional derivative would be . Would you like to calculate this dot product?

[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="4.1"] i.e the co-ordinates involving partial derivative of . So, Then (Ans) .

# Similar Problems

[/et_pb_text][et_pb_post_slider include_categories="12" image_placement="left" _builder_version="4.1"][/et_pb_post_slider][et_pb_divider _builder_version="3.22.4" background_color="#0c71c3"][/et_pb_divider][/et_pb_column][/et_pb_row][/et_pb_section]

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