What is the derivative of 3x^2cos(5x) ?

The derivative of 3x^2cos(5x) is 3(2xcos(5x)-5x^2sin(5x))

What is the first derivative of 3x^2cos(5x) ?

The first derivative of 3x^2cos(5x) is 3(2xcos(5x)-5x^2sin(5x))

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derivative of

3 x^{2} cos (5 x)

3 (2 x cos (5 x) - 5 x^{2} sin (5 x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= 3 (2 x cos (5 x) - 5 x^{2} sin (5 x))

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