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)-sec^2(x))(sec(x)-tan(x))^{1/2}

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)-sec^2(x))(sec(x)-tan(x))^{1/2}

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

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

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)) = sec (x) tan (x) - sec^{2} (x)

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

Simplify

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

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

x^{2} - 11, 10 x, [- 11, 0] y = 0

\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

x \frac{d y}{d x} = e^{y + x}

f (x) = x - x^{3}, (1, 0)

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)-sec^2(x))(sec(x)-tan(x))^{1/2}
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)-sec^2(x))(sec(x)-tan(x))^{1/2}