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Popular >

derivative of sqrt(sin(3x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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f^{^{'}} (x) = - \frac{4 x}{( 1 + 2 x ^{2} ) ^{2}}

(6y+2x-7)dx+(4y+6x-1)dy=0

(6 y + 2 x - 7) d x + (4 y + 6 x - 1) d y = 0

integral from-1 to 1 of 2-|x|

\int_{- 1}^{1} 2 - ∣ x ∣ d x

integral of 1/(e^{-t)}

\int \frac{1}{e ^{- t}} d t

integral of 4cos^3(6x)

\int 4 cos^{3} (6 x) d x

Frequently Asked Questions (FAQ)

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