What is the derivative of f(x)=6sin^3(sqrt(x)) ?

The derivative of f(x)=6sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of f(x)=6sin^3(sqrt(x)) ?

The first derivative of f(x)=6sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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derivative of

f (x) = 6 sin^{3} (x)

\frac{9 sin ^{2} ( x ) cos ( x )}{x}

Solution steps

\frac{d}{d x} (6 sin^{3} (x))

Take the constant out:

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

= 6 \frac{d}{d x} (sin^{3} (x))

Apply the chain rule:

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

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

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

= 6 \cdot 3 (sin (x))^{2} \frac{cos ( x )}{2 x}

Simplify

6 \cdot 3 sin^{2} (x) \frac{cos ( x )}{2 x} : \frac{9 sin ^{2} ( x ) cos ( x )}{x}

= \frac{9 sin ^{2} ( x ) cos ( x )}{x}

\int 8 x^{2} + 6 + \frac{9}{x ^{2} + 1} d x

y^{^{''}} + 16 y^{^{'}} + 73 y = 0

y^{^{''}} - 8 y^{^{'}} + 4 y = 0

\frac{d y}{d x} = 2

\int e^{- x^{8}} (- 8 x^{7}) d x

What is the derivative of f(x)=6sin^3(sqrt(x)) ?
The derivative of f(x)=6sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of f(x)=6sin^3(sqrt(x)) ?
The first derivative of f(x)=6sin^3(sqrt(x)) is (9sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))