Question

Find an equation of the tangent line to the curve at the point (1, 1).

Answer 1

\[y=\ln(x e^{x^5})\]

Answer 2

Find the derivative with respect to x first.

Answer 3

http://www.wolframalpha.com/input/?i=deriv+ln%28xe^%28x^5%29%29

Answer 4

So there you go. Now just put in your x value of 1 to figure out the slope.

Answer 5

So that give you your slope, m. Now solve the equation 1 = m*1 + b for b.
The equation for the line is y = m*x + b

Answer 6

y=ln(x)+ln(e^(x^5))
y=ln(x)+x^5
dy/dx=1/x+5x^4

Answer 7

dy/dx = i/x +5x^4
at point(1,1) slope m=1/1 + 5(1)^4=6
y-y1=m(x-xi)
y-1=6(x-1)
y=6x-6+1
y=6x-5 ans......eq. of the tangent line at pt(1,1)