Use the Gradient to Find the Directional Derivative of the Function

question 72

Multiple Choice

Use the gradient to find the directional derivative of the function at P in the direction of Q. $f ( x , y ) = \sin ( 7 x ) \cos y , P ( 0,0 ) , Q \left( \frac { \pi } { 7 } , \pi \right)$

• A) \(\pi\)
• B) \(\pi ( \sin ( 7 x ) \cos y + \cos ( 7 x ) \sin y )\)
• C) \(\pi ( \cos ( 7 x ) \cos y - \sin ( 7 x ) \sin y )\)
• D) \(\frac { 1 } { \sqrt { 50 } }\)
• E) \(\frac { 7 } { \sqrt { 50 } }\)

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Definitions:

Secured

Ensured to be firmly attached or fastened so as to not give way or become lost.

Total Magnification

The overall enlargement of an image achieved by a microscope, calculated by multiplying the magnification of the ocular lens by that of the objective lens.

Oil-immersion Lens

A microscope objective lens designed to be used with a drop of immersion oil to increase magnification quality by reducing light refraction.

Compound Light Microscope

A microscope that uses a series of lenses to magnify objects in stages, including an objective lens near the specimen and an eyepiece to view the magnified image.