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Popular >

derivative of 3x^2cos(x)

Solution

\frac{d}{d x} (3 x^{2} cos (x))

Solution

3 (2 x cos (x) - x^{2} sin (x))

Solution steps

\frac{d}{d x} (3 x^{2} cos (x))

Take the constant out:

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

= 3 \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)

= 3 (\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)

= 3 (2 x cos (x) + (- sin (x)) x^{2})

Simplify

= 3 (2 x cos (x) - x^{2} sin (x))

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Frequently Asked Questions (FAQ)

What is the derivative of 3x^2cos(x) ?
The derivative of 3x^2cos(x) is 3(2xcos(x)-x^2sin(x))
What is the first derivative of 3x^2cos(x) ?
The first derivative of 3x^2cos(x) is 3(2xcos(x)-x^2sin(x))