What is the derivative of sqrt(9+3x+sin(3x)) ?

The derivative of sqrt(9+3x+sin(3x)) is (3cos(3x)+3)/(2sqrt(9+3x+sin(3x)))

What is the first derivative of sqrt(9+3x+sin(3x)) ?

The first derivative of sqrt(9+3x+sin(3x)) is (3cos(3x)+3)/(2sqrt(9+3x+sin(3x)))

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\frac{d}{d x} (9 + 3 x + sin (3 x))

\frac{3 cos ( 3 x ) + 3}{2 9 + 3 x + sin ( 3 x )}

Solution steps

\frac{d}{d x} (9 + 3 x + sin (3 x))

Apply the chain rule:

\frac{1}{2 9 + 3 x + sin ( 3 x )} \frac{d}{d x} (9 + 3 x + sin (3 x))

= \frac{1}{2 9 + 3 x + sin ( 3 x )} \frac{d}{d x} (9 + 3 x + sin (3 x))

\frac{d}{d x} (9 + 3 x + sin (3 x)) = 3 cos (3 x) + 3

= \frac{1}{2 9 + 3 x + sin ( 3 x )} (3 cos (3 x) + 3)

Simplify

\frac{1}{2 9 + 3 x + sin ( 3 x )} (3 cos (3 x) + 3) : \frac{3 cos ( 3 x ) + 3}{2 9 + 3 x + sin ( 3 x )}

= \frac{3 cos ( 3 x ) + 3}{2 9 + 3 x + sin ( 3 x )}

What is the derivative of sqrt(9+3x+sin(3x)) ?
The derivative of sqrt(9+3x+sin(3x)) is (3cos(3x)+3)/(2sqrt(9+3x+sin(3x)))
What is the first derivative of sqrt(9+3x+sin(3x)) ?
The first derivative of sqrt(9+3x+sin(3x)) is (3cos(3x)+3)/(2sqrt(9+3x+sin(3x)))