What is the derivative of 5(2xcos(7x-7x^2sin(7x))) ?

The derivative of 5(2xcos(7x-7x^2sin(7x))) is 5(2cos(7x)-28xsin(7x)-49x^2cos(7x))

What is the first derivative of 5(2xcos(7x-7x^2sin(7x))) ?

The first derivative of 5(2xcos(7x-7x^2sin(7x))) is 5(2cos(7x)-28xsin(7x)-49x^2cos(7x))

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\frac{d}{d x} (5 (2 x cos (7 x) - 7 x^{2} sin (7 x)))

5 (2 cos (7 x) - 28 x sin (7 x) - 49 x^{2} cos (7 x))

Solution steps

\frac{d}{d x} (5 (2 x cos (7 x) - 7 x^{2} sin (7 x)))

Take the constant out:

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

= 5 \frac{d}{d x} (2 x cos (7 x) - 7 x^{2} sin (7 x))

Apply the Sum/Difference Rule:

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

= 5 (\frac{d}{d x} (2 x cos (7 x)) - \frac{d}{d x} (7 x^{2} sin (7 x)))

\frac{d}{d x} (2 x cos (7 x)) = 2 (cos (7 x) - 7 x sin (7 x))

\frac{d}{d x} (7 x^{2} sin (7 x)) = 7 (2 x sin (7 x) + cos (7 x) \cdot 7 x^{2})

= 5 (2 (cos (7 x) - 7 x sin (7 x)) - 7 (2 x sin (7 x) + cos (7 x) \cdot 7 x^{2}))

Expand

2 (cos (7 x) - 7 x sin (7 x)) - 7 (2 x sin (7 x) + cos (7 x) \cdot 7 x^{2}) : 2 cos (7 x) - 28 x sin (7 x) - 49 x^{2} cos (7 x)

= 5 (2 cos (7 x) - 28 x sin (7 x) - 49 x^{2} cos (7 x))

\int cos^{3} (20 x) d x

y^{^{''}} + 2 y = sin (2 x), y (0) = 0, y^{^{'}} (0) = 0

x \to 2 + lim (\frac{∣ x ∣}{2 - x})

\int \frac{x ^{3} + 5 x ^{2} - 4}{x ^{2}} d x

\int 30 x + sin (x) + C d x

What is the derivative of 5(2xcos(7x-7x^2sin(7x))) ?
The derivative of 5(2xcos(7x-7x^2sin(7x))) is 5(2cos(7x)-28xsin(7x)-49x^2cos(7x))
What is the first derivative of 5(2xcos(7x-7x^2sin(7x))) ?
The first derivative of 5(2xcos(7x-7x^2sin(7x))) is 5(2cos(7x)-28xsin(7x)-49x^2cos(7x))