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Popular >

derivative of 9sin(xcos(x))

Solution

\frac{d}{d x} (9 sin (x) cos (x))

Solution

9 cos (2 x)

Solution steps

\frac{d}{d x} (9 sin (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

= 9 (cos (x) cos (x) + (- sin (x)) sin (x))

Simplify

9 (cos (x) cos (x) + (- sin (x)) sin (x)) : 9 cos (2 x)

= 9 cos (2 x)

Graph

Popular Examples

inverse oflaplace 1/(s^2+2^2)inverse laplace

\frac{1}{s ^{2} + 2 ^{2}}

(dx)/(dt)=-(5x)/(100)

\frac{d x}{d t} = - \frac{5 x}{100}

integral of sin(2x)-sin(x/2)

\int sin (2 x) - sin (\frac{x}{2}) d x

inverse oflaplace ((2s+3))/(s^2-2s+5)inverse laplace

\frac{( 2 s + 3 )}{s ^{2} - 2 s + 5}

y^{''}-6y^'-27y=-3e^{-3t}

y^{^{''}} - 6 y^{^{'}} - 27 y = - 3 e^{- 3 t}

Frequently Asked Questions (FAQ)

What is the derivative of 9sin(xcos(x)) ?
The derivative of 9sin(xcos(x)) is 9cos(2x)
What is the first derivative of 9sin(xcos(x)) ?
The first derivative of 9sin(xcos(x)) is 9cos(2x)