Hi i was wondering if someone could check my work for these couple questions:(adsbygoogle = window.adsbygoogle || []).push({});

Find dy/dx (do not simplify)

a)y=e^sin3x

dy/dx= e^sin3x (cos3x)(3)

=3cos3xe^sin3x

b)y=5^(square rootx) x^2

dy/dx=x5^(square rootx) (xln5+2)

c)y=ln(x^2 / (2x+5)^3 )

y=lnx^2 - ln(2x+5)^3

dy/dx= 2x/x^2 - 6(2x+5)^2 / (2x=5)^3

=2/x - 6/(2x+5)

d)y=4log base 2 (square rootx+1)

y=4logbase2 (x+1)^-1

dy/dx= 4/lnbase2(square rootx+1)

e)y=ln[x^2 - e^x / x^2 +e^x]

y= ln(x^2 -e^x) - ln(x^2 +e^x)

dy/dx= [2x -e^x / x^2 - e^x] - [2x +e^x / x^2+e^x]

f)e^x^2 multiplied by y^3=x (isolate dy/dx)

I am unsure of how to do this one, i have never seen one like this before, could someone show what i would do.

g)Use logarthimic differentiation to find dy/dx if

y=[e^x cosx / (square root x)]^5

lny=5xlne +5lncosx -5/2lnx

dy/dx= y[5x-5tanx-5/2x]

dy/dx= =[e^x cosx / (square root x)]^5 [5x-5tanx-5/2x]

h)A radioactive substance decays in such a way that the amount in grams present at time t years is given by A(t)=100e^-0.2t

i)What is the initial amount of radioactive material, A(0)?

A(0)= 100

ii)Find the rate of decay function, A'(t).

A'(t)=-20e^-0.2t

iii)How mucgh radio active material is present when t-50 years? How fast is the material decaying at this time?

A(50)=100e^-10

=0.0045399

A'(50)=-20e^-10

=-0.0009079

iv)At what time t is one half of the original substance remaining? What is the decay rate at this time?

I am not sure what to do here also if someone could show me how id really appreciate it.

*For this question and parts of the question i am not sure if some of my equations are correct as the numbers i am getting do not seem like it should be what they are.

j)solve the logarithmic equation logbase3(x-3) + logbase3(x) = logbase3(4)

I am also not sure what to do for this question.

Thanks in advanced for the help! If someone could show me how to do those few questions and check my work on those ones cuz my text book does not show what the answers are or how to do some of them.

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# Homework Help: Derivatives of Log and Exponential Functions

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