Question

find derivative of y= e^(sin(3x))

Answer 1

Answer:

e^(sin(3x)) * 3cos3x

Explanation:

dy/dx = d(e^(sin(3x))/dx

dy/dx = e^(sin(3x)) * d(sin3x)/dx

dy/dx = e^(sin(3x)) * 3cos3x

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Answer 2

The derivative of y is 3cos(3x)×e^sin(3x).

Given:

y= e^(sin(3x))

To Find:

The derivative of y.

Solution:

We are required to find the derivative of y.

The derivative of 'y' with respect to 'x' is given as

dy/dx = d(e^(sin(3x)))/dx   ----------(1)

We are going to use two derivative formulas here

1) d(e^f(x))/dx = e^f(x)×f'(x)  -------(2)

where f(x) = sin(3x)

f'(x) = d(sin(3x))/dx   --------(3)

2) d(sin(ax))/dx = a cos(ax)  

By using the above formula in equation(3) we get

f'(x) = 3 cos(3x)     [∵ a = 3]

Substitute the value of f(x) and f'(x) in equation(2) we get

d(e^f(x))/dx = 3 cos(3x)×e^sin(3x) Substitute in equation(1) we get

dy/dx = 3cos(3x)×e^sin(3x)

Therefore, The derivative of y is 3cos(3x)×e^sin(3x).

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