# Calculus

I am unsure of how to take the derivative of this equation. It may be the exponents that are giving me trouble but I'm not sure exactly.

Find the equation of the tangent line to the curve 4e^xy = 2x + y at point (0,4).

On the left side, is the "xy" the exponent of e, or do you mean 4(e^x)y ?

Use implicit differentiation to get the slope m = dy/dx at x=0, y=4.
If 4 e^(xy) = 2x + y, then
4 e^(xy)* (y + x dy/dx) = 2 + dy/dx
Solve for dy/dx = m. The tangent line equation is then
(y-4) = m x

the exponent of e is "xy".

It's must clearer now, thank you.

In that case, my derivation should be correct. Substitute x=0, y=4 in the equation
4 e^(xy)* (y + x dy/dx) = 2 + dy/dx
4*1*(4 + 0) = 2 + dy/dx
dy/dx = 14
y-4 = 14 x
y = 14 x + 4

1. 👍 0
2. 👎 0
3. 👁 94

## Similar Questions

1. ### Math

Could I please get some help for these 3 questions, apologies for asking so many, but they were the ones I was really unsure of: 1. Find an equation for the line tangent to y=ln(x) and that goes through the origin. I have no idea,

asked by Bob on January 6, 2016
2. ### Calculus

My question is with a multi-part homework assignment that we got in class. The information given is : A factory manufactures widgets. The rate of production of widgets after t weeks is widgets/ week. The equation for this is

asked by Noah on February 7, 2017
3. ### Calculus--> bobpursley

How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for

asked by Anonymous on May 30, 2007
4. ### Calc

1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)4 f"(x)>0 for all x I

asked by Aurora on June 20, 2007
5. ### 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
6. ### Math - derivative of sinusoidal (check)

a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x)

asked by Farah on November 29, 2010
7. ### CALCULUS HELP

Find the second derivative for the function 5x^3+60x^2-36x-41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative of

asked by Herosugar on September 26, 2012
8. ### Calculus

Both x and y denote functions of t that are related by the given equation. Use this equation and the given derivative information to find the specified derivative. Equation:35x^2+20y^2=1 Given that dx/dt=4, find dy/dt when

asked by Kelly on July 17, 2010
9. ### algebra

Hockey teams receive 2 points for a win and 1 point for a tie. The Wildcats once won a championship with 60 points. They won 9 more games than they tied. How many wins and how many ties did the Wildcats have? I'm a little unsure

asked by Nessie on February 10, 2009
10. ### physics (mechanics)

Practice problem: A rocket sled for testing equipment under large accelerations starts at rest and accelerates according to the expression: a= (2.8 m/s^3)t + (3.9 m/s^2) How far does the rocket move in the time interval t=0 to

asked by John on August 28, 2010

More Similar Questions