what is the derivative of the following functions with respect to x:(adsbygoogle = window.adsbygoogle || []).push({});

a) y = 5e^-4x ans: -20e ^-4x

b) y = 1/2e^x^2 ans: xe^x^2

c)y = x^4 e^x ans: 4x^3 e^x + x^4 e^x

d) y = e^-x (x) ans: - (x + 1)e^-x/(x^2)

e) y = (1 + e^x)^1/2 ans: e^x/[2(1 + e^x)^1/2]

f) y = x + e ^ (x)^1/2 ans: 1 + [e ^(x)^1/2 / 2(x)^1/2]

3a) what is the equation of the tangent to the curve at the specified

point?

a) y = e^2x at (1, e^2) ans: y = 2e^2x - e^2

b) y = e^x^2/(x) at (1, e) ans: y = x

4)a) what is d^2/y/dx^2

a) y = x^2 e^-x ans: (x^2 -4x +2)e^-x

b) y = 4xe^x^2 ans: (16 x^3 + 24 x)e^x^2

c) y = e^-x sin x ans: -2e^-x cos x

5) how do you show that if y = e^x cos 2x then

d^2y/dx - 2(dy/dx) + 5y = 0?

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How do you evaluate log (subcript 2) 1/32?

b) log (g) 32 + log g(16) ?

c) log (2) 3

how do you solve for x? are there restrictions?

a) log (x) 25 = 2/3

b) log(7) [x + 7] + log(7) [x-7] = 0

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# Calculus problems

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