What is the derivative of x^5sin^2(x) ?

The derivative of x^5sin^2(x) is 5x^4sin^2(x)+sin(2x)x^5

What is the first derivative of x^5sin^2(x) ?

The first derivative of x^5sin^2(x) is 5x^4sin^2(x)+sin(2x)x^5

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derivative of

x^{5} sin^{2} (x)

5 x^{4} sin^{2} (x) + sin (2 x) x^{5}

Solution steps

\frac{d}{d x} (x^{5} sin^{2} (x))

Apply the Product Rule:

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

f = x^{5}, g = sin^{2} (x)

= \frac{d}{d x} (x^{5}) sin^{2} (x) + \frac{d}{d x} (sin^{2} (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} sin^{2} (x) + sin (2 x) x^{5}

\frac{d}{d t} (cos (w_{0} \cdot t))

ln^{1} (+ x)

f (x) = 3 x^{2} - 2 x - 1

\frac{2}{sin ( x )}

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

What is the derivative of x^5sin^2(x) ?
The derivative of x^5sin^2(x) is 5x^4sin^2(x)+sin(2x)x^5
What is the first derivative of x^5sin^2(x) ?
The first derivative of x^5sin^2(x) is 5x^4sin^2(x)+sin(2x)x^5