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Popular >

derivative of y=sin(x)cos(x)

Solution

derivative of

y = sin (x) 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

slope of-2x+5 slope

- 2 x + 5

polar (-4sqrt(3),4)cartesian to polar

(- 43, 4)

slope of y=3 slope

y = 3

tangent of f(x)= 3/4 x^4-4/3 x^3+5/2 tangent of

f (x) = \frac{3}{4} x^{4} - \frac{4}{3} x^{3} + \frac{5}{2}

Convert to Rectangular Coordinates (2,270)polar to cartesian

(2, 270)

Frequently Asked Questions (FAQ)

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