What is (\partial)/(\partial x)(sin(x^3)+3xy) ?

The answer to (\partial)/(\partial x)(sin(x^3)+3xy) is cos(x^3)*3x^2+3y

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(\partial)/(\partial x)(sin(x^3)+3xy)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

l a pl a ce t r an s f or m t^{2} cos (4 t)

\int ye d y

\int cos (x) 9 - sin^{2} (x) d x

7 x y^{^{'}} - 2 y = \frac{- x ^{2}}{y ^{6}}

\frac{d}{d x} (5 x^{2} + 3 x)

What is (\partial)/(\partial x)(sin(x^3)+3xy) ?
The answer to (\partial)/(\partial x)(sin(x^3)+3xy) is cos(x^3)*3x^2+3y