Derivatives
Find the derivative of
f(x)=x^3
f'(x)=3x^2
Evaluate
\int 3 dx
3x+c
Evaluate
\int_0^2xdx
2
Find the derivative of
f(x)=(3x+4)^8
f'(x)=24(3x+4)^7
Evaluate
\int 3e^xdx
3e^x+c
Evaluate
\int_2^5e^xdx
e^5-e^2
Find the derivative of
f(x)=x^2e^x
f'(x)=2xe^x+x^2e^x
Evaluate
\int 2/xdx
2\ln|x|+c
Evaluate
\int_1^5 (1/x)dx
ln(5)
Find the derivative of
f(x)=\frac{x^2+2}{x^3}
f'(x)=-frac{1}{x^2}-\frac{6}{x^4}
Evaluate
\int e^{7x+4}dx
1/7e^{7x+4}+c
Evaluate
\int_1^3(3x^2+4x)dx
42
Find the derivative of
f(x)=frac{e^x}{\sqrt{x}}
f'(x)=frac{\sqrt{x}e^x-frac{1}{2}x^{-1/2}e^x}{x}
Evaluate
\int 1/(3x-4) dx
1/3\ln|3x-4|+c
Evaluate
\int_{-1}^4 (3x-2)/x dx
15-2ln(4)