What is the derivative of e^{sin(5x}) ?

The derivative of e^{sin(5x}) is e^{sin(5x)}cos(5x)*5

What is the first derivative of e^{sin(5x}) ?

The first derivative of e^{sin(5x}) is e^{sin(5x)}cos(5x)*5

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\frac{d}{d x} (e^{s i n (5 x)})

e^{s i n (5 x)} cos (5 x) \cdot 5

Solution steps

\frac{d}{d x} (e^{s i n (5 x)})

Apply the chain rule:

e^{s i n (5 x)} \frac{d}{d x} (sin (5 x))

= e^{s i n (5 x)} \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= e^{s i n (5 x)} cos (5 x) \cdot 5

\frac{\partial}{\partial x} (tan (x) + y)

\int cos^{4} (2 y) d y

cos (3 x) y^{^{'}} + 3 (tan (3 x)) y = sec (3 x)

\frac{\partial}{\partial x} (e^{- 2 x} cos (2 π t))

y^{^{'}} = \frac{( 4 - 2 x )}{( 3 + 2 y )}

What is the derivative of e^{sin(5x}) ?
The derivative of e^{sin(5x}) is e^{sin(5x)}cos(5x)*5
What is the first derivative of e^{sin(5x}) ?
The first derivative of e^{sin(5x}) is e^{sin(5x)}cos(5x)*5