   Chapter 14, Problem 32RE

Chapter
Section
Textbook Problem

Find du if u = ln(1 + se2t).

To determine

To find: The value of du if u=ln(1+se2t) .

Explanation

Chain Rule:

“Suppose that z=f(x,y) is a differentiable function of x and y , where x=g(t)andy=h(t) are both differentiable functions of t . Then, z is differentiable function of t and dzdt=zxdxdt+zydydt ”.

Calculation:

The given function is, u=ln(1+se2t) (1)

Take partial derivative with respect to s of the equation (1),

us=x(ln(1+se2t))=11+se2t(1)(e2t)=e2t1+se2t

Thus, the partial derivate, us=e2t1+se2t

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