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Popular >

derivative of 2x^2cos(x)

Solution

\frac{d}{d x} (2 x^{2} cos (x))

Solution

2 (2 x cos (x) - x^{2} sin (x))

Solution steps

\frac{d}{d x} (2 x^{2} cos (x))

Take the constant out:

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

= 2 \frac{d}{d x} (x^{2} cos (x))

Apply the Product Rule:

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

f = x^{2}, g = cos (x)

= 2 (\frac{d}{d x} (x^{2}) cos (x) + \frac{d}{d x} (cos (x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 (2 x cos (x) + (- sin (x)) x^{2})

Simplify

= 2 (2 x cos (x) - x^{2} sin (x))

Popular Examples

\frac{y ^{^{'}}}{y} = x

tangent of (6x)/(2+x^2)tangent of

\frac{6 x}{2 + x ^{2}}

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

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

derivative of f(x)=(2x+3)^{11}(4-5x)^9 derivative of

f (x) = (2 x + 3)^{11} (4 - 5 x)^{9}

limit as x approaches 1+of 1

x \to 1 + lim (1)

Frequently Asked Questions (FAQ)

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