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

The answer to (\partial)/(\partial x)(sqrt(2x^3+y^2)) is (3x^2)/(sqrt(2x^3+y^2))

Popular >

(\partial)/(\partial x)(sqrt(2x^3+y^2))

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

\frac{3 x ^{2}}{2 x ^{3} + y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 2 x ^{3} + y ^{2}} \frac{\partial}{\partial x} (2 x^{3} + y^{2})

= \frac{1}{2 2 x ^{3} + y ^{2}} \frac{\partial}{\partial x} (2 x^{3} + y^{2})

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

= \frac{1}{2 2 x ^{3} + y ^{2}} \cdot 6 x^{2}

Simplify

\frac{1}{2 2 x ^{3} + y ^{2}} \cdot 6 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + y ^{2}}

= \frac{3 x ^{2}}{2 x ^{3} + y ^{2}}

\frac{d}{d z} (\frac{1}{1 - z ^{- 1}})

\frac{d}{d y} (4 \cdot x^{2} \cdot y^{3} - 4)

y = (t^{2} - 7)^{2}

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

\frac{d}{d x} (8 arcsin (x^{4}))

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