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Popular >

derivative of sqrt(3x^2)sin(5x)

Solution

\frac{d}{d x} (3 x^{2} sin (5 x))

Solution

3 sin (5 x) + 53 x cos (5 x)

Solution steps

\frac{d}{d x} (3 x^{2} sin (5 x))

Apply the Product Rule:

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

f = 3 x^{2}, g = sin (5 x)

= \frac{d}{d x} (3 x^{2}) sin (5 x) + \frac{d}{d x} (sin (5 x)) 3 x^{2}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 3 sin (5 x) + cos (5 x) \cdot 5 3 x^{2}

3 x^{2} = 3 x

= 3 sin (5 x) + 53 x cos (5 x)

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(3x^2)sin(5x) ?
The derivative of sqrt(3x^2)sin(5x) is sqrt(3)sin(5x)+5sqrt(3)xcos(5x)
What is the first derivative of sqrt(3x^2)sin(5x) ?
The first derivative of sqrt(3x^2)sin(5x) is sqrt(3)sin(5x)+5sqrt(3)xcos(5x)