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Popular >

derivative of f(x)=sin(x)*cos(x)

Solution

derivative of

f (x) = sin (x) \cdot cos (x)

Solution

cos (2 x)

Solution steps

\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)

= \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)

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

Simplify

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

= cos (2 x)

Popular Examples

inverse oflaplace 3/(s^2+4)inverse laplace

\frac{3}{s ^{2} + 4}

laplacetransform cos(t-pi)laplace transform

cos (t - π)

area-2x^2+8,3x+1,x=0 area

- 2 x^{2} + 8, 3 x + 1, x = 0

7y^{''}+21y^'-28y=0

7 y^{^{''}} + 21 y^{^{'}} - 28 y = 0

limit as x approaches 0 of (x^3+1)/(x^5)

x \to 0 lim (\frac{x ^{3} + 1}{x ^{5}})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sin(x)*cos(x) ?
The derivative of f(x)=sin(x)*cos(x) is cos(2x)
What is the first derivative of f(x)=sin(x)*cos(x) ?
The first derivative of f(x)=sin(x)*cos(x) is cos(2x)