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

The answer to (\partial)/(\partial x)(3ysin(7y^2x)) is 21y^3cos(7y^2x)

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

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

21 y^{3} cos (7 y^{2} x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 y cos (7 y^{2} x) \cdot 7 y^{2} : 21 y^{3} cos (7 y^{2} x)

= 21 y^{3} cos (7 y^{2} x)

\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

\int_{0}^{\frac{1}{3}} \frac{4}{1 + 9 x ^{2}} d x

y = x^{3} - 2 x^{2} + 5

\int r ln (r) d r

x \to 1 lim (\frac{x ^{8} - 1}{x - 1})

What is (\partial)/(\partial x)(3ysin(7y^2x)) ?
The answer to (\partial)/(\partial x)(3ysin(7y^2x)) is 21y^3cos(7y^2x)