What is the derivative of 4sin^3(xcos(x)) ?

The derivative of 4sin^3(xcos(x)) is 12sin^2(x)-16sin^4(x)

What is the first derivative of 4sin^3(xcos(x)) ?

The first derivative of 4sin^3(xcos(x)) is 12sin^2(x)-16sin^4(x)

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\frac{d}{d x} (4 sin^{3} (x) cos (x))

12 sin^{2} (x) - 16 sin^{4} (x)

Solution steps

\frac{d}{d x} (4 sin^{3} (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (sin^{3} (x) cos (x))

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (sin^{3} (x)) cos (x) + \frac{d}{d x} (cos (x)) sin^{3} (x))

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

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

= 4 (3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x))

Simplify

4 (3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x)) : 12 sin^{2} (x) - 16 sin^{4} (x)

= 12 sin^{2} (x) - 16 sin^{4} (x)

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

\frac{d}{d x} ((x e^{x})^{π})

\int \frac{e ^{x}}{3 + e ^{x}} d x

\int ln (13 t) d t

\int r^{2} (r^{3} - 2)^{2} d r

What is the derivative of 4sin^3(xcos(x)) ?
The derivative of 4sin^3(xcos(x)) is 12sin^2(x)-16sin^4(x)
What is the first derivative of 4sin^3(xcos(x)) ?
The first derivative of 4sin^3(xcos(x)) is 12sin^2(x)-16sin^4(x)