What is the derivative of 3x^2cos(6x) ?

The derivative of 3x^2cos(6x) is 3(2xcos(6x)-6x^2sin(6x))

What is the first derivative of 3x^2cos(6x) ?

The first derivative of 3x^2cos(6x) is 3(2xcos(6x)-6x^2sin(6x))

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\frac{d}{d x} (3 x^{2} cos (6 x))

3 (2 x cos (6 x) - 6 x^{2} sin (6 x))

Solution steps

\frac{d}{d x} (3 x^{2} cos (6 x))

Take the constant out:

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

= 3 \frac{d}{d x} (x^{2} cos (6 x))

Apply the Product Rule:

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

f = x^{2}, g = cos (6 x)

= 3 (\frac{d}{d x} (x^{2}) cos (6 x) + \frac{d}{d x} (cos (6 x)) x^{2})

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

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= 3 (2 x cos (6 x) + (- sin (6 x) \cdot 6) x^{2})

Simplify

= 3 (2 x cos (6 x) - 6 x^{2} sin (6 x))

s (t) = 4 2 t^{2} - 4 t + 7

\int (2 x - 5 x^{2}) (2 - 10 x) d x

\int \frac{x + 1}{2 x ^{2} - 6 x + 4} d x

\frac{d}{d x} (2 π (\frac{x}{9.8})^{\frac{1}{2}})

\int x^{2} + 2 x + 4 d x

What is the derivative of 3x^2cos(6x) ?
The derivative of 3x^2cos(6x) is 3(2xcos(6x)-6x^2sin(6x))
What is the first derivative of 3x^2cos(6x) ?
The first derivative of 3x^2cos(6x) is 3(2xcos(6x)-6x^2sin(6x))