What is (\partial)/(\partial x)(sqrt(t^4+x^3)) ?

The answer to (\partial)/(\partial x)(sqrt(t^4+x^3)) is (3x^2)/(2sqrt(t^4+x^3))

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(\partial)/(\partial x)(sqrt(t^4+x^3))

\frac{\partial}{\partial x} (t^{4} + x^{3})

\frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

Solution steps

\frac{\partial}{\partial x} (t^{4} + x^{3})

Treat

t

as a constant

Apply the chain rule:

\frac{1}{2 t ^{4} + x ^{3}} \frac{\partial}{\partial x} (t^{4} + x^{3})

= \frac{1}{2 t ^{4} + x ^{3}} \frac{\partial}{\partial x} (t^{4} + x^{3})

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

= \frac{1}{2 t ^{4} + x ^{3}} \cdot 3 x^{2}

Simplify

\frac{1}{2 t ^{4} + x ^{3}} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

= \frac{3 x ^{2}}{2 t ^{4} + x ^{3}}

\int 4 cos (x) d x

\int \frac{1}{22 - x ^{2}} d x

n = 0 \sum \infty 6 (\frac{1}{7})^{n}

x \to 2 - lim (\frac{x + 2}{x - 4})

n = - \infty \sum \infty 7^{2}

What is (\partial)/(\partial x)(sqrt(t^4+x^3)) ?
The answer to (\partial)/(\partial x)(sqrt(t^4+x^3)) is (3x^2)/(2sqrt(t^4+x^3))