What is (\partial)/(\partial x)(4y^8+3y^2x^2) ?

The answer to (\partial)/(\partial x)(4y^8+3y^2x^2) is 6y^2x

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(\partial)/(\partial x)(4y^8+3y^2x^2)

\frac{\partial}{\partial x} (4 y^{8} + 3 y^{2} x^{2})

6 y^{2} x

Solution steps

\frac{\partial}{\partial x} (4 y^{8} + 3 y^{2} x^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 y^{8}) + \frac{\partial}{\partial x} (3 y^{2} x^{2})

\frac{\partial}{\partial x} (4 y^{8}) = 0

\frac{\partial}{\partial x} (3 y^{2} x^{2}) = 6 y^{2} x

= 0 + 6 y^{2} x

Simplify

= 6 y^{2} x

(x^{2} + y^{2}) d x = 2 x y d y

ln (1 + e^{- x})

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

\int sin (t) d t

\frac{d}{d x} (a \cdot x^{2} + b \cdot x + c)

What is (\partial)/(\partial x)(4y^8+3y^2x^2) ?
The answer to (\partial)/(\partial x)(4y^8+3y^2x^2) is 6y^2x