What is the derivative of (1+sin(x)sin(x)) ?

The derivative of (1+sin(x)sin(x)) is cos(x)+sin(2x)

What is the first derivative of (1+sin(x)sin(x)) ?

The first derivative of (1+sin(x)sin(x)) is cos(x)+sin(2x)

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\frac{d}{d x} ((1 + sin (x)) sin (x))

cos (x) + sin (2 x)

Solution steps

\frac{d}{d x} ((1 + sin (x)) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + sin (x), g = sin (x)

= \frac{d}{d x} (1 + sin (x)) sin (x) + \frac{d}{d x} (sin (x)) (1 + sin (x))

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

= cos (x) sin (x) + cos (x) (1 + sin (x))

Simplify

cos (x) sin (x) + cos (x) (1 + sin (x)) : cos (x) + sin (2 x)

= cos (x) + sin (2 x)

What is the derivative of (1+sin(x)sin(x)) ?
The derivative of (1+sin(x)sin(x)) is cos(x)+sin(2x)
What is the first derivative of (1+sin(x)sin(x)) ?
The first derivative of (1+sin(x)sin(x)) is cos(x)+sin(2x)