derivative of y = eu is = eu , where u is a function of x. Here we will use the Quotient
Rule to find the derivative: f′(x) = . This can be simplified to f′(x) =
.
- f′(x) =
The rule for finding the derivative of y = loga u is , and the rule for finding the
derivative of y = au is = au (ln a) , where u is a function of x. Before we find the
derivative, we can use the laws of logarithms to simplify the logarithm. We get f(x) =
log10^3 x. Now if you are alert, you will remember that log 10^3 x = 3x, so this simplifies to f(x) =
3 x = x. The derivative is simply f′(x) = .
- f′(x) = 3e^3 x − 3ex(e)(ln 3)
The rule for finding the derivative of y = eu is = eu , and the rule for finding the
derivative of y = au is = au(ln a) , where u is a function of x. We get f′(x) = 3e^3 x − 3ex(e)
(ln3).
- f′(x) = 10sin x(cos x)(ln 10)
The rule for finding the derivative of y = au is = au(ln a) , where u is a function of x. We
get f′(x) = 10sin x(cos x)(ln 10).
- f′(x) = ln 10
Before we find the derivative, we can use the laws of logarithms to simplify the logarithm. We
get f(x) = ln(10x) = x ln 10. Now the derivative is simply f′(x) = ln 10.
- f′(x) = x^45 x(5 + x ln 5)
