What is the slope of the line tangent to the curve y = arctan(4x) where x = 1/4?

The slope of the line tangent to the curve y = arctan(4x) where x = 1/4 is 2

Given the function

The slope of the function can be given by differentiating the function as shown below;

On differentiating the given function

Substitute x = 1/4 into the result to have:

Hence the slope of the line tangent to the curve y = arctan(4x) where x = 1/4 is 2

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: