Thread: Simple Differentiation

How do I exactly differentiate 3^(5x)

Thanxx a lot!

Originally Posted by xwrathbringerx

How do I exactly differentiate 3^(5x)

Thanxx a lot!

The general fromula for f= a^(u(x))

f ' = ln(a) a^(u(x))du/dx

For 3^(5x)

f ' = ln(3)3^(5x)5 = 5ln(3)3^(5x)

doesn't make sense as x ' = 1

(a^x ) ' = ln(a)*a^x period

for a^(u(x) use the chain rule to obtain

f ' = ln(a) a^(u(x))du/dx

A general method for problems like this is to take the logarithm of both sides. If then . Now differentiate both sides with respect to x.

The derivative of ln(y) with respect to y is but since y itself is a function of x, by the chain rule, the derivative of ln(y) with respect to x is .

so .