# Calculus

Find the derivative of:
y= 5^x + 15/x^6

I'm assuming I need to take the natural log of each side, but I get stuck after that part.

1. 👍 0
2. 👎 0
3. 👁 49
1. I would split it into two problems and add the result.

y = 5^x
ln y = x ln 5
y'/y = ln 5
y' = y ln 5
y' = 5^x ln 5
then
y = 15 x^-6
y' = 15(-6) x^-7
y' = -90/x^7
so finally
y' = 5^x ln 5 - 90/x^7

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Math

I understand generally how to solve, by taking natural logs and the the derivative, but i am confused by the presence of the 3 in front... if f(x)= 3(sin(x))^x, find f'(1) should i move 3 to the y side or take the natural log of

asked by Tokey on November 5, 2010
2. ### calc

derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of

asked by MARY on May 6, 2007
3. ### Math (Calculus)

y= x^(2x+1) find the derivative of the function using natural log

asked by Amanda on May 7, 2008
4. ### Calculus - derivatives

Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the

asked by Lucy X on November 29, 2009
5. ### Calculus

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2

asked by Anonymous on February 24, 2015
6. ### Calculus

R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the

asked by Anonymous on May 29, 2007
7. ### Calculus (Help)

Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took

asked by Confused on February 21, 2007
8. ### Chain Rule

Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x

asked by Matt on September 26, 2007
9. ### Calculus

Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x

asked by Matt on September 30, 2007
10. ### Calculus

For 0 < x < PI/2, if y = sin(x)^x, then dy/dx is.. I understand that you can take the natural logarithm of both sides and then take the derivative but why can't I simply take the derivative of it and get.. dy/dx =

asked by Anonymous on March 30, 2008

More Similar Questions