What is the derivative of f(x)=4sin^2(5x+3) ?

The derivative of f(x)=4sin^2(5x+3) is 40sin(5x+3)cos(5x+3)

What is the first derivative of f(x)=4sin^2(5x+3) ?

The first derivative of f(x)=4sin^2(5x+3) is 40sin(5x+3)cos(5x+3)

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derivative of

f (x) = 4 sin^{2} (5 x + 3)

40 sin (5 x + 3) cos (5 x + 3)

Solution steps

\frac{d}{d x} (4 sin^{2} (5 x + 3))

Take the constant out:

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

= 4 \frac{d}{d x} (sin^{2} (5 x + 3))

Apply the chain rule:

2 sin (5 x + 3) \frac{d}{d x} (sin (5 x + 3))

= 2 sin (5 x + 3) \frac{d}{d x} (sin (5 x + 3))

\frac{d}{d x} (sin (5 x + 3)) = cos (5 x + 3) \cdot 5

= 4 \cdot 2 sin (5 x + 3) cos (5 x + 3) \cdot 5

Simplify

= 40 sin (5 x + 3) cos (5 x + 3)

What is the derivative of f(x)=4sin^2(5x+3) ?
The derivative of f(x)=4sin^2(5x+3) is 40sin(5x+3)cos(5x+3)
What is the first derivative of f(x)=4sin^2(5x+3) ?
The first derivative of f(x)=4sin^2(5x+3) is 40sin(5x+3)cos(5x+3)