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Popular >

derivative of y=arccos(e^{3x})

Solution

derivative of

y = arccos (e^{3 x})

Solution

- \frac{3 e ^{3 x}}{1 - e ^{6 x}}

Solution steps

\frac{d}{d x} (arccos (e^{3 x}))

Apply the chain rule:

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

= - \frac{1}{1 - ( e ^{3 x} ) ^{2}} \frac{d}{d x} (e^{3 x})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= - \frac{1}{1 - ( e ^{3 x} ) ^{2}} e^{3 x} \cdot 3

Simplify

- \frac{1}{1 - ( e ^{3 x} ) ^{2}} e^{3 x} \cdot 3 : - \frac{3 e ^{3 x}}{1 - e ^{6 x}}

= - \frac{3 e ^{3 x}}{1 - e ^{6 x}}

Popular Examples

area cos(3x),2-cos(x)area

cos (3 x), 2 - cos (x)

derivative of f(x)=x^3-3x^2-45x+5 derivative of

f (x) = x^{3} - 3 x^{2} - 45 x + 5

(1 - \frac{1}{x})^{^{'}}

y^{''}-3/t y^'+(20)/(t^2)y=0

y^{^{''}} - \frac{3}{t} y^{^{'}} + \frac{20}{t ^{2}} y = 0

derivative of arcsin(2x-3)derivative of

arcsin (2 x - 3)

Frequently Asked Questions (FAQ)

What is the derivative of y=arccos(e^{3x}) ?
The derivative of y=arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}
What is the first derivative of y=arccos(e^{3x}) ?
The first derivative of y=arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}