What is (\partial)/(\partial x)(6y^5sin(3x)) ?

The answer to (\partial)/(\partial x)(6y^5sin(3x)) is 18y^5cos(3x)

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(\partial)/(\partial x)(6y^5sin(3x))

\frac{\partial}{\partial x} (6 y^{5} sin (3 x))

18 y^{5} cos (3 x)

Solution steps

\frac{\partial}{\partial x} (6 y^{5} sin (3 x))

Treat

y

as a constant

Take the constant out:

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

= 6 y^{5} \frac{\partial}{\partial x} (sin (3 x))

Apply the chain rule:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

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

= 6 y^{5} cos (3 x) \cdot 3

Simplify

= 18 y^{5} cos (3 x)

y = (x^{2} + 5 x + 2)^{3}

x \to \frac{c}{2 ^{-}} lim ([2 x - 4])

(y^{2} + x y^{2}) y^{^{'}} = 1

g (x) = \frac{3 x + 1}{( 2 x ^{2} - 5 ) ^{2}}

(1 + e^{t})^{2}

What is (\partial)/(\partial x)(6y^5sin(3x)) ?
The answer to (\partial)/(\partial x)(6y^5sin(3x)) is 18y^5cos(3x)