What is (\partial)/(\partial x)(6y^5sin(2x)) ?

The answer to (\partial)/(\partial x)(6y^5sin(2x)) is 12y^5cos(2x)

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(\partial)/(\partial x)(6y^5sin(2x))

\frac{\partial}{\partial x} (6 y^{5} sin (2 x))

12 y^{5} cos (2 x)

Solution steps

\frac{\partial}{\partial x} (6 y^{5} sin (2 x))

Treat

y

as a constant

Take the constant out:

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

= 6 y^{5} \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

cos (2 x) \frac{\partial}{\partial x} (2 x)

= cos (2 x) \frac{\partial}{\partial x} (2 x)

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

= 6 y^{5} cos (2 x) \cdot 2

Simplify

= 12 y^{5} cos (2 x)

\frac{d}{d x} (\frac{x ^{3}}{x ^{2} - 1})

\int arctan (2 t) d t

x \to + 4 lim (3)

y^{^{''}} - 3 y^{^{'}} + 4 y = 0

\frac{d}{d x} (\frac{( 4 x - 2 ) ^{4}}{3 x ^{2} + 7})

What is (\partial)/(\partial x)(6y^5sin(2x)) ?
The answer to (\partial)/(\partial x)(6y^5sin(2x)) is 12y^5cos(2x)