What is the derivative of 7(sin(x^2)+2x^2cos(x^2)) ?

The derivative of 7(sin(x^2)+2x^2cos(x^2)) is 7(6xcos(x^2)-4x^3sin(x^2))

What is the first derivative of 7(sin(x^2)+2x^2cos(x^2)) ?

The first derivative of 7(sin(x^2)+2x^2cos(x^2)) is 7(6xcos(x^2)-4x^3sin(x^2))

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derivative of

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

7 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 7 (cos (x^{2}) \cdot 2 x + 2 (2 x cos (x^{2}) - 2 x^{3} sin (x^{2})))

Expand

cos (x^{2}) \cdot 2 x + 2 (2 x cos (x^{2}) - 2 x^{3} sin (x^{2})) : 6 x cos (x^{2}) - 4 x^{3} sin (x^{2})

= 7 (6 x cos (x^{2}) - 4 x^{3} sin (x^{2}))

\frac{d}{d x} (5 x^{3} y^{2} + x^{2} sin (y^{2}))

\int \frac{11 x ^{4} + 11 x ^{3} + 2 x + 1}{x ^{2} + x} d x

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

x \to 0 lim (- 10 x)

\frac{\partial}{\partial x} (x^{2} sin (x))

What is the derivative of 7(sin(x^2)+2x^2cos(x^2)) ?
The derivative of 7(sin(x^2)+2x^2cos(x^2)) is 7(6xcos(x^2)-4x^3sin(x^2))
What is the first derivative of 7(sin(x^2)+2x^2cos(x^2)) ?
The first derivative of 7(sin(x^2)+2x^2cos(x^2)) is 7(6xcos(x^2)-4x^3sin(x^2))