# Math (Calculus)

posted by .

y= x^(2x+1)

find the derivative of the function using natural log

• Math (Calculus) -

Log(y) = (2x+1)Log(x)

Differentiate both sides:

y'/y = 2 Log(x) + 2 + 1/x

Multiply by y:

y' = [2 Log(x) + 2 + 1/x] x^(2x+1)

• Math (Calculus) -

y=x2x+1

Find the derivative of the expression.

(2x+1)

To find the derivative of 2x, multiply the base (x) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, x is eliminated from the term.

1

Since 1 does not contain x, the derivative of 1 is 0.

2x+1=2+0

Add 0 to 2 to get 2.

2x+1=2

Using the chain rule, the derivative of x2x+1 is

x2x+1*2

Multiply x2x+1 by 2 to get 2x2x+1.

2x2x+1

The derivative of y with respect to x is 2x2x+1.

The derivative of y with respect to x is 2x2x+1.

## Similar Questions

1. ### Calc

a) y =ln(x-1) find dy/dx=? b) y=3 ln x - ln (1/x) where x >0, dy/dx= ?
2. ### Calculus derivatives

f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.
3. ### calculus

You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function?
4. ### 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 it?
5. ### 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.
6. ### calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)
7. ### calculus

use implicit differentiation to find dy/dx . Then evaluate the derivative function at the designated point. log (xy)= 2; (4, 25)
8. ### calculus

find the derivative of the function y=log absolut power 2-x
9. ### Math

h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h^-1(x) = My work so far h(x) = log(6x+5/7x-4) y=log(6x+5/7x-4) x=log(6y+5/7y-4) 7xy-4x= log(6y+5) how would I solve from here. Would I solve for y then do the …
10. ### Calculus

What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like?

More Similar Questions