What is the derivative of 3x^2sin(x+3xcos(x)) ?

The derivative of 3x^2sin(x+3xcos(x)) is 3x^2cos(x)+3xsin(x)+3cos(x)

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

The first derivative of 3x^2sin(x+3xcos(x)) is 3x^2cos(x)+3xsin(x)+3cos(x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (3 x cos (x)) = 3 (cos (x) - x sin (x))

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

Simplify

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

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

\frac{d}{d t} (a cos (3 t) + b sin (3 t))

\frac{\partial}{\partial a} (\frac{a}{sin ( θ )})

\frac{d}{d x} (x arctan (x))

x \frac{d y}{d x} = y + x^{2} + y^{2}

\int sin^{3} (x) x d x

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