What is the derivative of 6(sec(x+tan(x))^{3/2}) ?

The derivative of 6(sec(x+tan(x))^{3/2}) is -(9(sec(x)+tan(x))^{1/2})/(-1+sin(x))

What is the first derivative of 6(sec(x+tan(x))^{3/2}) ?

The first derivative of 6(sec(x+tan(x))^{3/2}) is -(9(sec(x)+tan(x))^{1/2})/(-1+sin(x))

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\frac{d}{d x} (6 (sec (x) + tan (x))^{\frac{3}{2}})

- \frac{9 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{- 1 + sin ( x )}

Solution steps

\frac{d}{d x} (6 (sec (x) + tan (x))^{\frac{3}{2}})

Take the constant out:

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

= 6 \frac{d}{d x} ((sec (x) + tan (x))^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (sec (x) + tan (x))

= \frac{3 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (sec (x) + tan (x))

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= 6 \cdot \frac{3 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{2} (- \frac{1}{- 1 + sin ( x )})

Simplify

6 \cdot \frac{3 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{2} (- \frac{1}{- 1 + sin ( x )}) : - \frac{9 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{- 1 + sin ( x )}

= - \frac{9 ( sec ( x ) + tan ( x ) ) ^{\frac{1}{2}}}{- 1 + sin ( x )}

\frac{\partial}{\partial x} (x^{5} sin (y))

\int x cos (7 x^{2}) d x

\frac{d}{d x} (\frac{x}{x})

\int_{0}^{1} 3 + 9 x^{2} d x

\frac{d}{d x} (\frac{e ^{x}}{9 x})

What is the derivative of 6(sec(x+tan(x))^{3/2}) ?
The derivative of 6(sec(x+tan(x))^{3/2}) is -(9(sec(x)+tan(x))^{1/2})/(-1+sin(x))
What is the first derivative of 6(sec(x+tan(x))^{3/2}) ?
The first derivative of 6(sec(x+tan(x))^{3/2}) is -(9(sec(x)+tan(x))^{1/2})/(-1+sin(x))