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` |
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