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Popular >

derivative of sin(3xcos(x))

Solution

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

Solution

3 cos (3 x) cos (x) - sin (x) sin (3 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (3 x), g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

= cos (3 x) \cdot 3 cos (x) + (- sin (x)) sin (3 x)

Simplify

= 3 cos (3 x) cos (x) - sin (x) sin (3 x)

Graph

Popular Examples

integral of (9x^2-7)

\int (9 x^{2} - 7) d x

integral of (-2y-2)/(y^2+y)

\int \frac{- 2 y - 2}{y ^{2} + y} d y

limit as x approaches 0-of x/(|x+1|)

x \to 0 - lim (\frac{x}{∣ x + 1 ∣})

integral of (16x^2)/((x-12)(x+4)^2)

\int \frac{16 x ^{2}}{( x - 12 ) ( x + 4 ) ^{2}} d x

integral of (1/8)y_{1}e^{-(y_{1}+y_{2})/2}_{1}

\int (\frac{1}{8}) y_{1} e^{- \frac{y _{1} + y _{2}}{2}} d y_{1}

Frequently Asked Questions (FAQ)

What is the derivative of sin(3xcos(x)) ?
The derivative of sin(3xcos(x)) is 3cos(3x)cos(x)-sin(x)sin(3x)
What is the first derivative of sin(3xcos(x)) ?
The first derivative of sin(3xcos(x)) is 3cos(3x)cos(x)-sin(x)sin(3x)