What is the derivative of sin(x+sin(7x)) ?

The derivative of sin(x+sin(7x)) is cos(x+sin(7x))(1+cos(7x)*7)

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

The first derivative of sin(x+sin(7x)) is cos(x+sin(7x))(1+cos(7x)*7)

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\frac{d}{d x} (sin (x + sin (7 x)))

cos (x + sin (7 x)) (1 + cos (7 x) \cdot 7)

Solution steps

\frac{d}{d x} (sin (x + sin (7 x)))

Apply the chain rule:

cos (x + sin (7 x)) \frac{d}{d x} (x + sin (7 x))

= cos (x + sin (7 x)) \frac{d}{d x} (x + sin (7 x))

\frac{d}{d x} (x + sin (7 x)) = 1 + cos (7 x) \cdot 7

= cos (x + sin (7 x)) (1 + cos (7 x) \cdot 7)

What is the derivative of sin(x+sin(7x)) ?
The derivative of sin(x+sin(7x)) is cos(x+sin(7x))(1+cos(7x)*7)
What is the first derivative of sin(x+sin(7x)) ?
The first derivative of sin(x+sin(7x)) is cos(x+sin(7x))(1+cos(7x)*7)