What is the derivative of 1/((25-x^2)) ?

The derivative of 1/((25-x^2)) is (2x)/((25-x^2)^2)

What is the first derivative of 1/((25-x^2)) ?

The first derivative of 1/((25-x^2)) is (2x)/((25-x^2)^2)

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\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

\frac{2 x}{( 25 - x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{( 25 - x ^{2} )})

Apply exponent rule:

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

= \frac{d}{d x} ((25 - x^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

= - \frac{1}{( 25 - x ^{2} ) ^{2}} \frac{d}{d x} (25 - x^{2})

\frac{d}{d x} (25 - x^{2}) = - 2 x

= - \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x)

Simplify

- \frac{1}{( 25 - x ^{2} ) ^{2}} (- 2 x) : \frac{2 x}{( 25 - x ^{2} ) ^{2}}

= \frac{2 x}{( 25 - x ^{2} ) ^{2}}

\int e^{7} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'}} = 8 x + y, y (0) = 1

\frac{d y}{d x} = \frac{2 x y - y ^{2}}{x ^{2}}

\frac{d y}{d x} = \frac{4 x ^{3}}{cos ( y )}

What is the derivative of 1/((25-x^2)) ?
The derivative of 1/((25-x^2)) is (2x)/((25-x^2)^2)
What is the first derivative of 1/((25-x^2)) ?
The first derivative of 1/((25-x^2)) is (2x)/((25-x^2)^2)