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derivative of f(x)=x^2cos(x)

Solution

derivative of

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

Solution

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

Solution steps

\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)

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

Simplify

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

Popular Examples

\frac{d}{d y} (e^{y})

derivative of sqrt(sin(3x))

\frac{d}{d x} (sin (3 x))

f^'(x)=-(4x)/((1+2x^2)^2)

f^{^{'}} (x) = - \frac{4 x}{( 1 + 2 x ^{2} ) ^{2}}

(6y+2x-7)dx+(4y+6x-1)dy=0

(6 y + 2 x - 7) d x + (4 y + 6 x - 1) d y = 0

integral from-1 to 1 of 2-|x|

\int_{- 1}^{1} 2 - ∣ x ∣ d x

Frequently Asked Questions (FAQ)

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