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Popular >

derivative of sin(x)*cos(x)

Solution

derivative of

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

integral of-sin(x)*cos^2(x)

\int - sin (x) \cdot cos^{2} (x) d x

integral of 1/(x^2sqrt(4x^2-9))

\int \frac{1}{x ^{2} 4 x ^{2} - 9} d x

(\partial)/(\partial y)(y-2)

\frac{\partial}{\partial y} (y - 2)

derivative of (1.01)^x+0.33^x derivative of

(1.01)^{x} + 0.3 3^{x}

derivative of 4*(3/2)^x derivative of

4 \cdot (\frac{3}{2})^{x}

Frequently Asked Questions (FAQ)

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