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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x ^{3} + sin ( 3 y )} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + sin ( 3 y )}

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

\int \frac{1}{x ^{2} + c} d x

\frac{2}{( s - 4 ) ^{3}}

\int_{- π}^{π} sin (k x) cos (n x) d x

x^{^{'}} = a x - b x^{2}

x \to - 1 lim (\frac{f ( x )}{x + 1})

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