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Popular >

f^'(x)=-2ln(x)+x^2-4+e^x+x^e

Solution

f^{^{'}} (x) = - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e}

Solution

f (x) = \frac{x ^{3}}{3} - 2 x ln (x) - 2 x + \frac{1}{e + 1} x^{e + 1} + e^{x} + c_{1}

Solution steps

f^{'} (x) = - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e} d x

\int - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e} d x = \frac{x ^{3}}{3} - 2 x ln (x) - 2 x + \frac{1}{e + 1} x^{e + 1} + e^{x} + c_{1}

f (x) = \frac{x ^{3}}{3} - 2 x ln (x) - 2 x + \frac{1}{e + 1} x^{e + 1} + e^{x} + c_{1}

Graph

Popular Examples

area f(x)=x^2-6x+8,g(x)=-2x+8 area

f (x) = x^{2} - 6 x + 8, g (x) = - 2 x + 8

y^{''}+8y^'+16=0

y^{^{''}} + 8 y^{^{'}} + 16 = 0

derivative of w^{3/2}(w+ce^w)derivative of

w^{\frac{3}{2}} (w + c e^{w})

derivative of ln(x^3+3)

\frac{d}{d x} (ln (x^{3} + 3))

limit as x approaches 0 of x/(x-1)

x \to 0 lim (\frac{x}{x - 1})

Frequently Asked Questions (FAQ)

What is the solution for f^'(x)=-2ln(x)+x^2-4+e^x+x^e ?
The solution for f^'(x)=-2ln(x)+x^2-4+e^x+x^e is f(x)=(x^3)/3-2xln(x)-2x+1/(e+1)x^{e+1}+e^x+c_{1}