What is (\partial)/(\partial x)(3sqrt(xy^2+9x)) ?

The answer to (\partial)/(\partial x)(3sqrt(xy^2+9x)) is (3(y^2+9))/(2sqrt(xy^2+9x))

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(\partial)/(\partial x)(3sqrt(xy^2+9x))

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

\frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}

Solution steps

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{\partial}{\partial x} (x y^{2} + 9 x)

Apply the chain rule:

\frac{1}{2 x y ^{2} + 9 x} \frac{\partial}{\partial x} (x y^{2} + 9 x)

= \frac{1}{2 x y ^{2} + 9 x} \frac{\partial}{\partial x} (x y^{2} + 9 x)

\frac{\partial}{\partial x} (x y^{2} + 9 x) = y^{2} + 9

= 3 \cdot \frac{1}{2 x y ^{2} + 9 x} (y^{2} + 9)

Simplify

3 \cdot \frac{1}{2 x y ^{2} + 9 x} (y^{2} + 9) : \frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}

= \frac{3 ( y ^{2} + 9 )}{2 x y ^{2} + 9 x}

f (x) = x \cdot 2 x + 2

y^{^{'}} = e^{(x + y)}

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\int_{0}^{π} 6 sin (x) d x

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What is (\partial)/(\partial x)(3sqrt(xy^2+9x)) ?
The answer to (\partial)/(\partial x)(3sqrt(xy^2+9x)) is (3(y^2+9))/(2sqrt(xy^2+9x))