What is (\partial)/(\partial x)(y^5sin(4x)) ?

The answer to (\partial)/(\partial x)(y^5sin(4x)) is y^5cos(4x)*4

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(\partial)/(\partial x)(y^5sin(4x))

\frac{\partial}{\partial x} (y^{5} sin (4 x))

y^{5} cos (4 x) \cdot 4

Solution steps

\frac{\partial}{\partial x} (y^{5} sin (4 x))

Treat

y

as a constant

Take the constant out:

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

= y^{5} \frac{\partial}{\partial x} (sin (4 x))

Apply the chain rule:

cos (4 x) \frac{\partial}{\partial x} (4 x)

= cos (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= y^{5} cos (4 x) \cdot 4

y (x + 7) + y^{^{'}} = 0, y (- 14) = 1

\frac{d}{d x} (7 cos (7 x))

\int_{0}^{2 π} x sin (x) d x

\int - 7 x d x

x \to - 2 + lim (\frac{x + 2}{x ^{3} + 8})

What is (\partial)/(\partial x)(y^5sin(4x)) ?
The answer to (\partial)/(\partial x)(y^5sin(4x)) is y^5cos(4x)*4