Friday

March 6, 2015

March 6, 2015

Posted by **Aurora** on Monday, June 11, 2007 at 8:26pm.

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

**Answer this Question**

**Related Questions**

calculus - how do you find the derivative of (X^2(2+x^1/2))/x^4. I'm confused ...

Calculus - find derivitive of 1/square root of x 1/square root of x = x^(-1/2) ...

Calculus--> bobpursley - How do you get m=0? from taking the second ...

Calculus - Area of rectangle = xy = x(4r^2 - x^2) Take the derivative. I am ...

calculus - This is from our problem set. f(x)= 2(x^3)-3(x^2)-12x+20 write an ...

Calculus - If x = t^2 + 1 and y = t^3, then d^2y/dx^2 = I know I can solve for t...

calculus - Find the first and second derivative - simplify your answer. y=x/4x+1...

Calculus - I am not sure what to do here: Find the derivative (f '(x) using the ...

Calc - 1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a ...

Calculus derivative - find the slope m and an equation of the tangent line to ...