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Popular >

derivative of y=arccsc(e^{9t})

Solution

derivative of

y = arccsc (e^{9 t})

Solution

- \frac{9}{e ^{18 t} - 1}

Solution steps

\frac{d}{d t} (arccsc (e^{9 t}))

Apply the chain rule:

- \frac{1}{( e ^{9 t} ) ^{2} ( e ^{9 t} ) ^{2} - 1} \frac{d}{d t} (e^{9 t})

= - \frac{1}{( e ^{9 t} ) ^{2} ( e ^{9 t} ) ^{2} - 1} \frac{d}{d t} (e^{9 t})

\frac{d}{d t} (e^{9 t}) = e^{9 t} \cdot 9

= - \frac{1}{( e ^{9 t} ) ^{2} ( e ^{9 t} ) ^{2} - 1} e^{9 t} \cdot 9

Simplify

- \frac{1}{( e ^{9 t} ) ^{2} ( e ^{9 t} ) ^{2} - 1} e^{9 t} \cdot 9 : - \frac{9}{e ^{18 t} - 1}

= - \frac{9}{e ^{18 t} - 1}

Popular Examples

integral of-8/(sqrt(x^2+16))

\int - \frac{8}{x ^{2} + 16} d x

tangent of f(x)=8e^{-0.5x},\at x=7 tangent of

f (x) = 8 e^{- 0.5 x}, at x = 7

(\partial)/(\partial x)(4xsin(xy))

\frac{\partial}{\partial x} (4 x sin (x y))

derivative of-2/((x-2^2))

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

limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)}

x \to 2 lim ((\frac{x + 3}{2 x + 1})^{\frac{2}{x - 2}})

Frequently Asked Questions (FAQ)

What is the derivative of y=arccsc(e^{9t}) ?
The derivative of y=arccsc(e^{9t}) is -9/(sqrt(e^{18t)-1)}
What is the first derivative of y=arccsc(e^{9t}) ?
The first derivative of y=arccsc(e^{9t}) is -9/(sqrt(e^{18t)-1)}