What is (\partial)/(\partial x)(7x^3cos(7x^2y)) ?

The answer to (\partial)/(\partial x)(7x^3cos(7x^2y)) is 7(3x^2cos(7x^2y)-14x^4ysin(7x^2y))

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(\partial)/(\partial x)(7x^3cos(7x^2y))

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

7 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

Solution steps

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

Treat

y

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (x^{3} cos (7 x^{2} y))

Apply the Product Rule:

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

f = x^{3}, g = cos (7 x^{2} y)

= 7 (\frac{\partial}{\partial x} (x^{3}) cos (7 x^{2} y) + \frac{\partial}{\partial x} (cos (7 x^{2} y)) x^{3})

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

\frac{\partial}{\partial x} (cos (7 x^{2} y)) = - sin (7 x^{2} y) \cdot 14 y x

= 7 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3})

Simplify

7 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3}) : 7 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

= 7 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 1)

\int_{- 2}^{3} \frac{22}{x ^{4}} d x

\frac{1}{3}

\int 343 x^{2} cos (7 x) d x

\frac{e ^{x}}{x + 1}, at x = 0

What is (\partial)/(\partial x)(7x^3cos(7x^2y)) ?
The answer to (\partial)/(\partial x)(7x^3cos(7x^2y)) is 7(3x^2cos(7x^2y)-14x^4ysin(7x^2y))