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Popular >

derivative of sin^2(3x+cos(5x^2))

Solution

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

Solution

3 sin (6 x) - sin (5 x^{2}) \cdot 10 x

Solution steps

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin^{2} (3 x)) + \frac{d}{d x} (cos (5 x^{2}))

\frac{d}{d x} (sin^{2} (3 x)) = 3 sin (6 x)

\frac{d}{d x} (cos (5 x^{2})) = - sin (5 x^{2}) \cdot 10 x

= 3 sin (6 x) - sin (5 x^{2}) \cdot 10 x

Popular Examples

integral from 0 to infinity of e^{-2t}

\int_{0}^{\infty} e^{- 2 t} d t

integral of (x+2)(x^2+4x+2)^{10}

\int (x + 2) (x^{2} + 4 x + 2)^{10} d x

\int - 64 d x

sum from n=1 to infinity of (-0.2)^{n-1}

n = 1 \sum \infty (- 0.2)^{n - 1}

derivative of x^2sqrt(2x-7)

\frac{d}{d x} (x^{2} 2 x - 7)

Frequently Asked Questions (FAQ)

What is the derivative of sin^2(3x+cos(5x^2)) ?
The derivative of sin^2(3x+cos(5x^2)) is 3sin(6x)-sin(5x^2)*10x
What is the first derivative of sin^2(3x+cos(5x^2)) ?
The first derivative of sin^2(3x+cos(5x^2)) is 3sin(6x)-sin(5x^2)*10x