What is the derivative of 3sin^5(x) ?

The derivative of 3sin^5(x) is 15sin^4(x)cos(x)

What is the first derivative of 3sin^5(x) ?

The first derivative of 3sin^5(x) is 15sin^4(x)cos(x)

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\frac{d}{d x} (3 sin^{5} (x))

15 sin^{4} (x) cos (x)

Solution steps

\frac{d}{d x} (3 sin^{5} (x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin^{5} (x))

Apply the chain rule:

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

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

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

= 3 \cdot 5 (sin (x))^{4} cos (x)

Simplify

= 15 sin^{4} (x) cos (x)

\frac{d}{d x} ((x + 1) (x + 2))

\frac{\partial}{\partial x} (y^{2} - 2 y cos (x))

\frac{d}{d t} (v (t))

\frac{d}{d x} (\frac{f ( x )}{g ( x )})

y^{^{''}} + 9 y = 2 cos (3 x)

What is the derivative of 3sin^5(x) ?
The derivative of 3sin^5(x) is 15sin^4(x)cos(x)
What is the first derivative of 3sin^5(x) ?
The first derivative of 3sin^5(x) is 15sin^4(x)cos(x)