What is the derivative of f(x)=sin^2(x)cos(x) ?

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

What is the first derivative of f(x)=sin^2(x)cos(x) ?

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

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derivative of

f (x) = sin^{2} (x) cos (x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

- x e^{- x} + e^{- x}

y = e^{- x} - e^{- x} x

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

\int 2 x x - \frac{1}{x} d x

\frac{d}{d x} (ln (52 x))

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