Find the derivative of `h(x)=ln10x+log_4 10x`
- print Print
- list Cite
Expert Answers
lfryerda
| Certified Educator
calendarEducator since 2012
write738 answers
starTop subjects are Math and Science
To find the derivative of this function, we need to change the base of the second term into base e, and then apply normal derivative rules.
`h(x)=ln 10x+log_4 10x` change base of second term
`=ln 10x+{ln 10x}/{ln4}` now expand both terms using multiplcation rule
`=ln 10+ln x+ln10/ln4+lnx/ln4` now differentiate
`h'(x)=0+1/x+0+1/{xln4}`
The derivative is `h'(x)=1/x+1/{xln4}` .
Related Questions
- Find the derivative of the function. h(x) = `x^(2)arctan 5x`
- 1 Educator Answer
- Use the four step process to find the derivative of f(x) where f'(x) = lim [f(x+h)-f(x)]/h (the...
- 1 Educator Answer
- The limit represents the derivative of some function f(x) at some number a. Find f and a. lim...
- 1 Educator Answer
- Find the 100th derivative of xe^x
- 1 Educator Answer
- Find the derivative of f(x) = 1+tan(x) / 1-tan(x)
- 2 Educator Answers
islnds | Student
Its not suppose to be 410 in the question. The 4 is suppose the be a subscript. It was typed that way initially, but somehow when the question got finalized it became 410.
button33 | Student
h'(x)=(1/x)+(1/x ln4)
Student Answers