What is (\partial)/(\partial x)(1/(xcos(z))) ?

The answer to (\partial)/(\partial x)(1/(xcos(z))) is -1/(x^2cos(z))

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(\partial)/(\partial x)(1/(xcos(z)))

\frac{\partial}{\partial x} (\frac{1}{x cos ( z )})

- \frac{1}{x ^{2} cos ( z )}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x cos ( z )})

Treat

z

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

= \frac{1}{cos ( z )} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= \frac{1}{cos ( z )} (- 1 \cdot x^{- 1 - 1})

Simplify

\frac{1}{cos ( z )} (- 1 \cdot x^{- 1 - 1}) : - \frac{1}{x ^{2} cos ( z )}

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

\int \frac{3 x}{2 e ^{6 x}} d x

\int_{0}^{5} \frac{1}{x ^{\frac{15}{14}}} d x

\frac{d}{d x} (ln (x - 4 y))

f (x) = (x^{3} + 3) e^{x}

\frac{1}{6} x^{2} - 3 x + 15

What is (\partial)/(\partial x)(1/(xcos(z))) ?
The answer to (\partial)/(\partial x)(1/(xcos(z))) is -1/(x^2cos(z))