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Popular >

derivative of arccos(e^{6x})

Solution

\frac{d}{d x} (arccos (e^{6 x}))

Solution

- \frac{6 e ^{6 x}}{1 - e ^{12 x}}

Solution steps

\frac{d}{d x} (arccos (e^{6 x}))

Apply the chain rule:

- \frac{1}{1 - ( e ^{6 x} ) ^{2}} \frac{d}{d x} (e^{6 x})

= - \frac{1}{1 - ( e ^{6 x} ) ^{2}} \frac{d}{d x} (e^{6 x})

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= - \frac{1}{1 - ( e ^{6 x} ) ^{2}} e^{6 x} \cdot 6

Simplify

- \frac{1}{1 - ( e ^{6 x} ) ^{2}} e^{6 x} \cdot 6 : - \frac{6 e ^{6 x}}{1 - e ^{12 x}}

= - \frac{6 e ^{6 x}}{1 - e ^{12 x}}

Popular Examples

integral of (6t^2+4t)(t^3+t^2+1)^6

\int (6 t^{2} + 4 t) (t^{3} + t^{2} + 1)^{6} d t

limit as x approaches-2-of x+2

x \to - 2 - lim (x + 2)

y^{''}+6y^'+8y=e^{5x},y(0)=2

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{5 x}, y (0) = 2

(dy)/(dx)+7y=12

\frac{d y}{d x} + 7 y = 12

parity sqrt((sin(x))/(1-sin(x)))parity

\frac{sin ( x )}{1 - sin ( x )}

Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{6x}) ?
The derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}
What is the first derivative of arccos(e^{6x}) ?
The first derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}