Logarithmic and exponential functions - Worksheet

Differentiate the following logarithmic and exponential functions:

`10 ln(x) + 6e^x - 5log_10(x)`		`10/x + 6e^x - 5/(x ln(10))`
`{ln(x)}/{e^x} + {e^x}/{ln(x)}`		`({e^x}/{x} - ln(x) e^x)(1/{e^{2x}} -1/{ln(x)}^2)`
`e^{10*x} + ln{10*x}`		`10e^(10x) + 1/x`
`x^3 * ln(x) + 4x^2ln(x)`		`x^2 +3x^2ln(x) + 4x +8xln(x)`
`ln(x^3 +2x) + e^x`		`(3x^2 + 2)/(x^3 + 2x) + e^x`
`ln(x) + ln(3)`		`1/x + 1`
`e^x + e^10`		`e^x + 1`
`{log_5(x)}/{log_6(x)} + 2^x ln(x)`		`log_6(x)/(x ln(5)) + 2^x/x + 2 2^x ln(x)`
`ln(x^3) + e^(3x)`		`3/x + 3e^(3x)`
`(1 + e^x)/(1 - e^x) + 2 ln(x)`		`((1 - e^x)(e^x) + (e^x)(1 + e^x))/((1 - e^x)^2) + 2/x`