If you invest p dollars in a bank account at an annual interest rate of r%, then

Question

If you invest p dollars in a bank account at an annual interest rate of r%, then after t years you will have B dollars, where B = p(1 + r/100)^t (a) Find dB/dp assuming r and t are constant. Use lower case letters. dB/dp = (b) Find dB/dr assuming p and t are constant. Use lower case letters. dB/dr = (c) Find dB/dt assuming p and r are constant. Use lower case letters. dB/dt = Use g(x) = e^x + e^-x/2 to find the following derivatives. (a) g'(x) = (b) d/dx (g(x^3)) = (c) d/dx (g(x))^5 = On a side note, g(x) = e^x + e^-x/2 is also known as the hyperbolic function cosh(x).

Explanation / Answer

given B =p(1+ r/100)t

a)dB/dp =1*(1+ r/100)t

dB/dp =(1+ r/100)t

b)dB/dr =p*t*(1+ r/100)t-1*(0+ 1/100)

dB/dr =(pt/100)(1+ r/100)t-1

c)dB/dt =p(1+ r/100)t *ln(1+ r/100)

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given g(x)=(ex+e-x)/2

a)g'(x)=(ex +e-x*(-1))/2

g'(x)=(ex -e-x)/2

b)d/dx(g(x3))

=d/dx((ex^3+e-x^3)/2)

=((ex^3*3x2 +e-x^3*(-3x2))/2)

=3x2 (ex^3-e-x^3)/2

c)d/dx(g(x))5

=d/dx((ex+e-x)/2)5

=5((ex+e-x)/2)5-1((ex +e-x*(-1))/2)

=5((ex+e-x)/2)4((ex -e-x)/2)

=5(ex+e-x)4(ex -e-x)/32

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