What is the derivative of sin(x+sin(10x)) ?

The derivative of sin(x+sin(10x)) is cos(x+sin(10x))(1+cos(10x)*10)

What is the first derivative of sin(x+sin(10x)) ?

The first derivative of sin(x+sin(10x)) is cos(x+sin(10x))(1+cos(10x)*10)

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\frac{d}{d x} (sin (x + sin (10 x)))

cos (x + sin (10 x)) (1 + cos (10 x) \cdot 10)

Solution steps

\frac{d}{d x} (sin (x + sin (10 x)))

Apply the chain rule:

cos (x + sin (10 x)) \frac{d}{d x} (x + sin (10 x))

= cos (x + sin (10 x)) \frac{d}{d x} (x + sin (10 x))

\frac{d}{d x} (x + sin (10 x)) = 1 + cos (10 x) \cdot 10

= cos (x + sin (10 x)) (1 + cos (10 x) \cdot 10)

What is the derivative of sin(x+sin(10x)) ?
The derivative of sin(x+sin(10x)) is cos(x+sin(10x))(1+cos(10x)*10)
What is the first derivative of sin(x+sin(10x)) ?
The first derivative of sin(x+sin(10x)) is cos(x+sin(10x))(1+cos(10x)*10)