What is the derivative of (sin(5x)^2) ?

The derivative of (sin(5x)^2) is 5sin(10x)

What is the first derivative of (sin(5x)^2) ?

The first derivative of (sin(5x)^2) is 5sin(10x)

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\frac{d}{d x} ((sin (5 x))^{2})

5 sin (10 x)

Solution steps

\frac{d}{d x} ((sin (5 x))^{2})

Apply the chain rule:

2 sin (5 x) \frac{d}{d x} (sin (5 x))

= 2 sin (5 x) \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 2 sin (5 x) cos (5 x) \cdot 5

Simplify

2 sin (5 x) cos (5 x) \cdot 5 : 5 sin (10 x)

= 5 sin (10 x)

\frac{d}{d x} (\frac{1}{x ln ( x )})

x \to 0 - lim (1 + x e^{x})

x \to - 1 lim (\frac{3 x}{x ^{2} + 1})

\frac{\partial}{\partial x} (6 x y - 6 x)

x \to 7 lim (4 x)

What is the derivative of (sin(5x)^2) ?
The derivative of (sin(5x)^2) is 5sin(10x)
What is the first derivative of (sin(5x)^2) ?
The first derivative of (sin(5x)^2) is 5sin(10x)