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In detail and complete 40 in detail...5 star rating

f(x) = x2 In x f(x) = x In f(x) = f(x) = In x/x f(x) = In (x + 1/x - 1) f(x) = ex In x f(x) = e-2x + x3 f(t) = t2 In g(s) = (ex + s + 1) (2e-s + s) F(x) = In(2x3 - 5x +1) h(t) = et + t/In t g(u) = In (u2 - 1)3 f(x) = ex + e-x/2 h(x) = e-x/x2 f(t) = f(x) = ex + e-x/ex - e-x f(x) = In(e-x + x) f(s) = es + In s g(u) = In(u + ) L(x) = In[x2 + 2x -3/x2 + 2x + 1] f(x) = 2x/x f(x) = x2 3x2 f(x) = x log10 x In Exercises 39 through 46, find the largest and smallest valures of the given function over the prescribed closed, bounded interval. f(x) = e1-x for 0 x 1 F(x) = ex2 - 2x for 0 x 2 f(x) = (3x - 1)e-x for 0 x 2 g(x) = ex/2x + 1 for 0 x 1 g(t) = t3/2 e-2t for 0 t 1 f(x) = e-2x -e-4x for 0 x 1 f(x) = In(x + 1)/x + 1 for 0 x 2 h(s) = 2s In s - s2 for 0.5 s 2 In Exercises 47 through 52, find an equation for the tangent line to y = f(x) at the specified point. f(x) = xe-x; where x = 0 f(x) = (x + 1)e-2x; where x = 0 f(x) = e2x/x2; where x = 1 f(x) = In x/x; where x = 1 f(x) = x2 In ; where x = 1 f(x) = x - In x; where x = e In Exercised 53 through 56, find the second derivative of the given function. f(x) = e2x + 2e-x f(x) = In(2x) + x2 f(t) = t2 In t g(t) = t2 e-t In Exercises 57 through 64, use logarithmic differentiation to find the derivative f'(x). f(x) = (2x + 3)2(x - 5x2)1/2 f(x) = x2 e-x(3x + 5)3 f(x) = 5x2

Show transcribed image text f(x) = x2 In x f(x) = x In f(x) = f(x) = In x/x f(x) = In (x + 1/x - 1) f(x) = ex In x f(x) = e-2x + x3 f(t) = t2 In g(s) = (ex + s + 1) (2e-s + s) F(x) = In(2x3 - 5x +1) h(t) = et + t/In t g(u) = In (u2 - 1)3 f(x) = ex + e-x/2 h(x) = e-x/x2 f(t) = f(x) = ex + e-x/ex - e-x f(x) = In(e-x + x) f(s) = es + In s g(u) = In(u + ) L(x) = In[x2 + 2x -3/x2 + 2x + 1] f(x) = 2x/x f(x) = x2 3x2 f(x) = x log10 x In Exercises 39 through 46, find the largest and smallest valures of the given function over the prescribed closed, bounded interval. f(x) = e1-x for 0 x 1 F(x) = ex2 - 2x for 0 x 2 f(x) = (3x - 1)e-x for 0 x 2 g(x) = ex/2x + 1 for 0 x 1 g(t) = t3/2 e-2t for 0 t 1 f(x) = e-2x -e-4x for 0 x 1 f(x) = In(x + 1)/x + 1 for 0 x 2 h(s) = 2s In s - s2 for 0.5 s 2 In Exercises 47 through 52, find an equation for the tangent line to y = f(x) at the specified point. f(x) = xe-x; where x = 0 f(x) = (x + 1)e-2x; where x = 0 f(x) = e2x/x2; where x = 1 f(x) = In x/x; where x = 1 f(x) = x2 In ; where x = 1 f(x) = x - In x; where x = e In Exercised 53 through 56, find the second derivative of the given function. f(x) = e2x + 2e-x f(x) = In(2x) + x2 f(t) = t2 In t g(t) = t2 e-t In Exercises 57 through 64, use logarithmic differentiation to find the derivative f'(x). f(x) = (2x + 3)2(x - 5x2)1/2 f(x) = x2 e-x(3x + 5)3 f(x) = 5x2