What is (\partial)/(\partial x)(pixsqrt(x^2+h^2)) ?

The answer to (\partial)/(\partial x)(pixsqrt(x^2+h^2)) is (pi(2x^2+h^2))/(sqrt(x^2+h^2))

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(\partial)/(\partial x)(pixsqrt(x^2+h^2))

\frac{\partial}{\partial x} (π x x^{2} + h^{2})

\frac{π ( 2 x ^{2} + h ^{2} )}{x ^{2} + h ^{2}}

Solution steps

\frac{\partial}{\partial x} (π x x^{2} + h^{2})

Take the constant out:

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

= π \frac{\partial}{\partial x} (x x^{2} + h^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + h^{2}

= π (\frac{\partial}{\partial x} (x) x^{2} + h^{2} + \frac{\partial}{\partial x} (x^{2} + h^{2}) x)

\frac{\partial}{\partial x} (x) = 1

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

= π (1 \cdot x^{2} + h^{2} + \frac{x}{x ^{2} + h ^{2}} x)

Simplify

π (1 \cdot x^{2} + h^{2} + \frac{x}{x ^{2} + h ^{2}} x) : \frac{π ( 2 x ^{2} + h ^{2} )}{x ^{2} + h ^{2}}

= \frac{π ( 2 x ^{2} + h ^{2} )}{x ^{2} + h ^{2}}

\int \frac{( e ^{x} - e ^{- x} )}{2} d x

x^{2} - 25 ln (x^{2})

2 e^{- t}

f (x) = - 9 x^{- \frac{1}{9}}

x \to - \infty lim (1 - e^{x})

What is (\partial)/(\partial x)(pixsqrt(x^2+h^2)) ?
The answer to (\partial)/(\partial x)(pixsqrt(x^2+h^2)) is (pi(2x^2+h^2))/(sqrt(x^2+h^2))