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