Homework Sourse1 find the derivative yln1ex1ex 2 find the derivative y ln e
1. find the derivative y=ln((1+e^x)/(1-e^x))
2. find the derivative y= ln e^x
3. find an equation of the tangent line to the
graph of the function at the given point f(x) = e^3 ln x, (1,0)
4. use implicit differentiation to find dy/dx e^(xy)+x^2-y^2=10
5. evaluate the definite integral. ?[2,0,x^2e^(3/2)] dx
2. find the derivative y= ln e^x
3. find an equation of the tangent line to the
graph of the function at the given point f(x) = e^3 ln x, (1,0)
4. use implicit differentiation to find dy/dx e^(xy)+x^2-y^2=10
5. evaluate the definite integral. ?[2,0,x^2e^(3/2)] dx
Solution
1) 2e^x/((1+e^x)(1-e^x)) 2) ln(e^x) = xlne = x y=x dy/dx=1 4) (-ye^(xy) -2x)/(xe^(xy)-2y) 5) x^2e^3/2 definite integral = e^(3/2)x^3/2 applying limits -4e^(3/2)
