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Popular >

derivative of sin(x*cos(x))

Solution

\frac{d}{d 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

y^{''}+9y=2cos(3x),y(0)=1,y^'(0)=0

y^{^{''}} + 9 y = 2 cos (3 x), y (0) = 1, y^{^{'}} (0) = 0

(\partial)/(\partial x)(x^2*e^{-2y})

\frac{\partial}{\partial x} (x^{2} \cdot e^{- 2 y})

(\partial)/(\partial x)(3y^2x)

\frac{\partial}{\partial x} (3 y^{2} x)

(\partial)/(\partial x)(6x^{7y})

\frac{\partial}{\partial x} (6 x^{7 y})

derivative of sin(x+sin(7x))

\frac{d}{d x} (sin (x + sin (7 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)