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

The derivative of-1/(x^2(sec^2(y))) is 2/(x^3sec^2(y))

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

The first derivative of-1/(x^2(sec^2(y))) is 2/(x^3sec^2(y))

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derivative of

- \frac{1}{x ^{2} ( sec ^{2} ( y ) )}

\frac{2}{x ^{3} sec ^{2} ( y )}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

- \frac{1}{sec ^{2} ( y )} (- 2 x^{- 2 - 1}) : \frac{2}{x ^{3} sec ^{2} ( y )}

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

What is the derivative of-1/(x^2(sec^2(y))) ?
The derivative of-1/(x^2(sec^2(y))) is 2/(x^3sec^2(y))
What is the first derivative of-1/(x^2(sec^2(y))) ?
The first derivative of-1/(x^2(sec^2(y))) is 2/(x^3sec^2(y))