What is the derivative of sin^7(2x) ?

The derivative of sin^7(2x) is 14sin^6(2x)cos(2x)

What is the first derivative of sin^7(2x) ?

The first derivative of sin^7(2x) is 14sin^6(2x)cos(2x)

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\frac{d}{d x} (sin^{7} (2 x))

14 sin^{6} (2 x) cos (2 x)

Solution steps

\frac{d}{d x} (sin^{7} (2 x))

Apply the chain rule:

7 (sin (2 x))^{6} \frac{d}{d x} (sin (2 x))

= 7 (sin (2 x))^{6} \frac{d}{d x} (sin (2 x))

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

= 7 (sin (2 x))^{6} cos (2 x) \cdot 2

Simplify

= 14 sin^{6} (2 x) cos (2 x)

\frac{d}{d x} (- 10 e^{- 2 x})

y = \frac{6 x}{7 - tan ( x )}

\int \frac{1}{1 + 2 y} d y

\int \frac{1}{x 3 - x ^{2}} d x

d y = x^{2} d x, y (0) = 0

What is the derivative of sin^7(2x) ?
The derivative of sin^7(2x) is 14sin^6(2x)cos(2x)
What is the first derivative of sin^7(2x) ?
The first derivative of sin^7(2x) is 14sin^6(2x)cos(2x)