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

The derivative of 6sin^6(sqrt(x)) is (18sin^5(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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

The first derivative of 6sin^6(sqrt(x)) is (18sin^5(sqrt(x))cos(sqrt(x)))/(sqrt(x))

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Popular >

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

\frac{18 sin ^{5} ( x ) cos ( x )}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

= 6 (sin (x))^{5} \frac{d}{d x} (sin (x))

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

= 6 \cdot 6 (sin (x))^{5} \frac{cos ( x )}{2 x}

Simplify

6 \cdot 6 sin^{5} (x) \frac{cos ( x )}{2 x} : \frac{18 sin ^{5} ( x ) cos ( x )}{x}

= \frac{18 sin ^{5} ( x ) cos ( x )}{x}

\int - 7 sin (7 x) d x

\int_{8}^{16} x 16 x - x^{2} d x

\frac{( 5 x - 25 )}{x ^{2} - 5 x}

y^{^{''}} + 4 y = - 12 sec (2 t)

y = 4 - 2 x - x^{- 3}

What is the derivative of 6sin^6(sqrt(x)) ?
The derivative of 6sin^6(sqrt(x)) is (18sin^5(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of 6sin^6(sqrt(x)) ?
The first derivative of 6sin^6(sqrt(x)) is (18sin^5(sqrt(x))cos(sqrt(x)))/(sqrt(x))