Posted by **Jean** on Wednesday, July 18, 2012 at 6:06pm.

Compute the derivative of f(x)=5^x^2+1 using logarithmic differentiation.

- Calc -
**Jean**, Wednesday, July 18, 2012 at 6:07pm
Check using the following formula:

(5^g(x))'= (ln5)*(5^g(x))*(g'(x))

- Calc -
**bobpursley**, Wednesday, July 18, 2012 at 6:22pm
I never did like formulas.

remember that derivative of ln(g(x))=g'(x)/g(x)

here f(x)=5^(x^2+1)

ln f(x)= (x^2+1)ln5

take the derivative

f'(x)/f(x)=2x*ln5 + 0

f'(x)=f(x)*10x*ln5=10x*ln5*5^(x^2+1)

Now comparing this to your 'formula':

f'(x)=ln5*5^(x^2+1)*2x=10x*5^(x^2+1)

Hmmm same thing.

## Answer this Question

## Related Questions

- calc - Use logarithmic differentiation to find the derivative of the function. y...
- calc - logarithmic differentiation of find derivative of y= square root of x^x
- Calculus - I need to find the derivative of the following problem via ...
- Math help! - Find derivative using logarithmic differentiation F(x)= secx^cotx
- collge calculus - find the derivative of y=[(4^(7x))(7^(4x))]/[10^(e)] without ...
- Calculus - Using logarithmic differentiation find the derivative of f(x)=2x/x. I...
- Calc - find the derivative of y =(x+3)^3 / sqrt(x^2 -1) using logarithmic ...
- calculus - Given y^4 -x^4=16 find and simplify d2y/dx2 using implicit ...
- Math - Use logarithmic differentiation to find the derivative of y: y=x^(e^x)
- Math - f(x)=x^5x Use logarithmic differentiation to determine the derivative.

More Related Questions