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

The derivative of 3(2xcos(5x)-5x^2sin(5x)) is 3(2cos(5x)-20xsin(5x)-25x^2cos(5x))

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

The first derivative of 3(2xcos(5x)-5x^2sin(5x)) is 3(2cos(5x)-20xsin(5x)-25x^2cos(5x))

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derivative of

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

3 (2 cos (5 x) - 20 x sin (5 x) - 25 x^{2} cos (5 x))

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (2 x cos (5 x)) = 2 (cos (5 x) - 5 x sin (5 x))

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

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

Expand

2 (cos (5 x) - 5 x sin (5 x)) - 5 (2 x sin (5 x) + cos (5 x) \cdot 5 x^{2}) : 2 cos (5 x) - 20 x sin (5 x) - 25 x^{2} cos (5 x)

= 3 (2 cos (5 x) - 20 x sin (5 x) - 25 x^{2} cos (5 x))

(0.2) (5.4)

\frac{\partial}{\partial x} (u^{7} + v^{7})

\frac{d}{d x} ((1 + x)^{\frac{1}{x}})

\int_{0}^{\frac{π}{2}} cos^{9} (x) d x

\frac{\partial}{\partial y} (- 2 + e^{- x} cos (y))

What is the derivative of 3(2xcos(5x)-5x^2sin(5x)) ?
The derivative of 3(2xcos(5x)-5x^2sin(5x)) is 3(2cos(5x)-20xsin(5x)-25x^2cos(5x))
What is the first derivative of 3(2xcos(5x)-5x^2sin(5x)) ?
The first derivative of 3(2xcos(5x)-5x^2sin(5x)) is 3(2cos(5x)-20xsin(5x)-25x^2cos(5x))