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

The derivative of sin^2(xcos^3(x)) is cos^3(x)sin(2x)-3sin^3(x)cos^2(x)

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

The first derivative of sin^2(xcos^3(x)) is cos^3(x)sin(2x)-3sin^3(x)cos^2(x)

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

cos^{3} (x) sin (2 x) - 3 sin^{3} (x) cos^{2} (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

sin (2 x) cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) sin^{2} (x) : cos^{3} (x) sin (2 x) - 3 sin^{3} (x) cos^{2} (x)

= cos^{3} (x) sin (2 x) - 3 sin^{3} (x) cos^{2} (x)

x \to 0 lim (x sin (\frac{4}{x}))

y^{^{'}} + y + 2 cos (x) = 0

\int_{4}^{6} \frac{1}{x} d x

x \to - 1 lim (x^{3} - 4 x + 1)

n = 10000 \sum \infty \frac{1}{n}

What is the derivative of sin^2(xcos^3(x)) ?
The derivative of sin^2(xcos^3(x)) is cos^3(x)sin(2x)-3sin^3(x)cos^2(x)
What is the first derivative of sin^2(xcos^3(x)) ?
The first derivative of sin^2(xcos^3(x)) is cos^3(x)sin(2x)-3sin^3(x)cos^2(x)