What is the derivative of sin^2(e^{3x+1}) ?

The derivative of sin^2(e^{3x+1}) is 6e^{3x+1}sin(e^{3x+1})cos(e^{3x+1})

What is the first derivative of sin^2(e^{3x+1}) ?

The first derivative of sin^2(e^{3x+1}) is 6e^{3x+1}sin(e^{3x+1})cos(e^{3x+1})

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\frac{d}{d x} (sin^{2} (e^{3 x + 1}))

6 e^{3 x + 1} sin (e^{3 x + 1}) cos (e^{3 x + 1})

Solution steps

\frac{d}{d x} (sin^{2} (e^{3 x + 1}))

Apply the chain rule:

2 sin (e^{3 x + 1}) \frac{d}{d x} (sin (e^{3 x + 1}))

= 2 sin (e^{3 x + 1}) \frac{d}{d x} (sin (e^{3 x + 1}))

\frac{d}{d x} (sin (e^{3 x + 1})) = cos (e^{3 x + 1}) e^{3 x + 1} \cdot 3

= 2 sin (e^{3 x + 1}) cos (e^{3 x + 1}) e^{3 x + 1} \cdot 3

Simplify

= 6 e^{3 x + 1} sin (e^{3 x + 1}) cos (e^{3 x + 1})

n = 0 \sum \infty \frac{3 ^{n}}{3 ^{n}}

\int \frac{x ^{3}}{x ^{4} - 3} d x

\int_{0}^{2} x^{2} - 1 d x

f (x) = - ln (x)

\int 5 x^{- 3} d x

What is the derivative of sin^2(e^{3x+1}) ?
The derivative of sin^2(e^{3x+1}) is 6e^{3x+1}sin(e^{3x+1})cos(e^{3x+1})
What is the first derivative of sin^2(e^{3x+1}) ?
The first derivative of sin^2(e^{3x+1}) is 6e^{3x+1}sin(e^{3x+1})cos(e^{3x+1})