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

The derivative of 4sin^3(sqrt(x)) is (6sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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

The first derivative of 4sin^3(sqrt(x)) is (6sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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

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

Solution steps

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

Take the constant out:

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

= 4 \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}

= 4 \cdot 3 (sin (x))^{2} \frac{cos ( x )}{2 x}

Simplify

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

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

(4 y + 8 t^{2}) d y + (16 y t - 3) d t = 0

\frac{\partial}{\partial x} (x^{2} sin (4 y))

\int x cos^{2} (x) d x

\frac{\partial}{\partial x} (- sin (x y) y)

y^{^{'}} - x y^{2} = 2 x y

What is the derivative of 4sin^3(sqrt(x)) ?
The derivative of 4sin^3(sqrt(x)) is (6sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of 4sin^3(sqrt(x)) ?
The first derivative of 4sin^3(sqrt(x)) is (6sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))