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

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

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

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

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

3 sin^{2} (x) - 4 sin^{4} (x)

Solution steps

\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)

= \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)

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

Simplify

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

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

r, r = tan (θ) sec (θ)

f (x) = 3 x^{7}

f (x) = \frac{x ^{4}}{9}

p (x) = 4 x^{2} - 1

f (x) = x^{2} - 5 x - 7

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