What is (\partial)/(\partial x)((a-b^2)/(x-c^2)) ?

The answer to (\partial)/(\partial x)((a-b^2)/(x-c^2)) is -(a-b^2)/((x-c^2)^2)

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(\partial)/(\partial x)((a-b^2)/(x-c^2))

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

- \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

Treat

a, b, c

as constants

Take the constant out:

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

= (a - b^{2}) \frac{\partial}{\partial x} (\frac{1}{x - c ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= (a - b^{2}) \frac{\partial}{\partial x} ((x - c^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( x - c ^{2} ) ^{2}} \frac{\partial}{\partial x} (x - c^{2})

= - \frac{1}{( x - c ^{2} ) ^{2}} \frac{\partial}{\partial x} (x - c^{2})

\frac{\partial}{\partial x} (x - c^{2}) = 1

= (a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1)

Simplify

(a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1) : - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

= - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

\frac{d}{d x} (5 - \frac{4}{x})

\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}

\frac{d}{d x} (sec (x^{5} + x))

(1.1) (0.5)

\int 1 + 5 x^{2} (10 x) d x

What is (\partial)/(\partial x)((a-b^2)/(x-c^2)) ?
The answer to (\partial)/(\partial x)((a-b^2)/(x-c^2)) is -(a-b^2)/((x-c^2)^2)