The derivative of the exponential function is, by definition, itself:
`d/(dx)e^x = e^x`.
With other bases, you have to multiply by the natural logarithm of the base:
`d/(dx)b^x = b^x*lnb`.
Let’s differentiate `3x^3(7)^(picos2x)`.
The first thing to notice is that we can use the product rule:
`d/(dx)3x^3(7)^(picos2x) = d/(dx)3x^3 * 7^(picos2x) + d/(dx)7^(picos2x) * 3x^3`,
which reduces to
`9x^2(7)^(picos2x) + 7^(picos2x)*ln7*d/(dx)picos2x`,
which then becomes
`(9x^2 + ln7d/(dx)picos2x)7^(picos2x)`,
giving us the final answer,
`(9x^2 - ln7*2pisin2x)7^(picos2x)`.