What is the derivative of sin(x+1+5x) ?

The derivative of sin(x+1+5x) is cos(x+1)+5

What is the first derivative of sin(x+1+5x) ?

The first derivative of sin(x+1+5x) is cos(x+1)+5

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\frac{d}{d x} (sin (x + 1) + 5 x)

cos (x + 1) + 5

Solution steps

\frac{d}{d x} (sin (x + 1) + 5 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (x + 1)) + \frac{d}{d x} (5 x)

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

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

= cos (x + 1) + 5

What is the derivative of sin(x+1+5x) ?
The derivative of sin(x+1+5x) is cos(x+1)+5
What is the first derivative of sin(x+1+5x) ?
The first derivative of sin(x+1+5x) is cos(x+1)+5