What is the derivative of (x^2+x^2sin^3(2x)) ?

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

What is the first derivative of (x^2+x^2sin^3(2x)) ?

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

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

2 (x^{2} + x) (2 x + 1) sin^{3} (2 x) + 6 sin^{2} (2 x) cos (2 x) (x^{2} + x)^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x^{2} + x)^{2}, g = sin^{3} (2 x)

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

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

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

= 2 (x^{2} + x) (2 x + 1) sin^{3} (2 x) + 6 sin^{2} (2 x) cos (2 x) (x^{2} + x)^{2}

x \to 0 lim (ln (x + e^{2 x}))

\int \frac{1}{x ^{2} + 6 x + 9} d x

x^{3} (x^{2} + 1)^{7}

x^{2} sin^{9} (+ x cos^{- 2} (x))

\int 3 x^{2} + 2 x - 3 d x

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