Ko'rsaatkich funksiya

Simple

100

f(x)=e^x

f′(x)=e^x

200

f(x)=2^x

f′(x)=2^x⋅ln2

300

f(x)=e^3x

f′(x)=3e^3x

400

f(x)=4^2x

f(x)=2⋅4^2x⋅ln4

500

f(x)=e^8x

f(x)=8e^8x

Normal

100

f(x)=3^x+2^x

f′(x)=3^x⋅ln3+2^x⋅ln2

200

f(x)=x⋅e^x

f′(x)=e^x(x+1)

300

f(x)=x²⋅ex^x

f'(x)=e^x(2x+x²) 

400

f(x)=e^x+4x

f′(x)=e^x+4

500

f(x)=2x⋅3x^x

f'(x)=2⋅3^x(1+xln3) 

Difficult

100

f(x)=x/e^x

f′(x)=1-x/e^x

200

f(x)=ln(3^x)

f′(x)=ln3

300

f(x)=e^{x^2}

f′(x)=2x⋅e^{x^2}

400

f(x)=e^x/x

f′(x)=e^x(1-x)/x²

500

f(x)=(2x+1)⋅5^x

f′(x)=5^x(2+(2x+1)ln5)