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Popular >

derivative of arccos(e^{7x})

Solution

derivative of

arccos (e^{7 x})

Solution

- \frac{7 e ^{7 x}}{1 - e ^{14 x}}

Solution steps

\frac{d}{d x} (arccos (e^{7 x}))

Apply the chain rule:

- \frac{1}{1 - ( e ^{7 x} ) ^{2}} \frac{d}{d x} (e^{7 x})

= - \frac{1}{1 - ( e ^{7 x} ) ^{2}} \frac{d}{d x} (e^{7 x})

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= - \frac{1}{1 - ( e ^{7 x} ) ^{2}} e^{7 x} \cdot 7

Simplify

- \frac{1}{1 - ( e ^{7 x} ) ^{2}} e^{7 x} \cdot 7 : - \frac{7 e ^{7 x}}{1 - e ^{14 x}}

= - \frac{7 e ^{7 x}}{1 - e ^{14 x}}

Popular Examples

integral from 0 to 1 of (x^3)/(x^2-x-6)

\int_{0}^{1} \frac{x ^{3}}{x ^{2} - x - 6} d x

inverse oflaplace 1/(s^2+40s+2000)inverse laplace

\frac{1}{s ^{2} + 40 s + 2000}

8t^2y^{''}-16y=11t^2-1

8 t^{2} y^{^{''}} - 16 y = 11 t^{2} - 1

derivative of sqrt(cot(3x))derivative of

cot (3 x)

tangent of f(x)=2x^3+3x^2-12x+6 tangent of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{7x}) ?
The derivative of arccos(e^{7x}) is -(7e^{7x})/(sqrt(1-e^{14x))}
What is the first derivative of arccos(e^{7x}) ?
The first derivative of arccos(e^{7x}) is -(7e^{7x})/(sqrt(1-e^{14x))}