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Popular >

derivative of ae^x+b/x+c/(x^2)

Solution

\frac{d}{d x} (a e^{x} + \frac{b}{x} + \frac{c}{x ^{2}})

Solution

a e^{x} - \frac{b}{x ^{2}} - \frac{2 c}{x ^{3}}

Solution steps

\frac{d}{d x} (a e^{x} + \frac{b}{x} + \frac{c}{x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a e^{x}) + \frac{d}{d x} (\frac{b}{x}) + \frac{d}{d x} (\frac{c}{x ^{2}})

\frac{d}{d x} (a e^{x}) = a e^{x}

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

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

= a e^{x} - \frac{b}{x ^{2}} - \frac{2 c}{x ^{3}}

Popular Examples

tangent of f(x)=7x^2-x^3,\at x=1 tangent of

f (x) = 7 x^{2} - x^{3}, at x = 1

integral from 0 to 1 of ln(4+x^2)

\int_{0}^{1} ln (4 + x^{2}) d x

integral of-ucos(2u)

\int - u cos (2 u) d u

integral of 1/([(x^2+9)^2])

\int \frac{1}{[ ( x ^{2} + 9 ) ^{2} ]} d x

derivative of (7^x/(x^3))

\frac{d}{d x} (\frac{7 ^{x}}{x ^{3}})

Frequently Asked Questions (FAQ)

What is the derivative of ae^x+b/x+c/(x^2) ?
The derivative of ae^x+b/x+c/(x^2) is ae^x-b/(x^2)-(2c)/(x^3)
What is the first derivative of ae^x+b/x+c/(x^2) ?
The first derivative of ae^x+b/x+c/(x^2) is ae^x-b/(x^2)-(2c)/(x^3)