Hello everyone! So my professor gave us 100 derivative problems for our review guide, and I am not sure how to do these ones, please help!

For these you have to find the derivative:

f(x) = ln(9 x+2)

h(x) = e^(x+38)

g(x) = 18^x

g(x) = (5 x^2 -7x)ln(x)

g(x) = (4 x- 6)^(0.5) ln(x)

h(x) = ln[(3x+1)/(4x-4)]

s(x) = ln(7 x - 5)^1.3

s(x) = log_3(9 x^2+4 x)

r(x) = [ln(38 x^2)]^2

r(x) = ln(x+4)+9 x^3 e^x

r(x) = e^(6 x+5)

r(x) = e^(5 x^2-6 x+1/x)

t(x) = 3^(6 x-2)


Find equation of the straight line tangent to the following curve at the point where x = 1. (Round all coefficients to two decimal places.) Use graphing technology to check your answer by plotting the given curve together with the tangent line.
y = ln sqrt(5 x^2+6)

Thanks a bunch!

So, basically all you need is the above and the chain rule.

For the first one, f(x) = ln(9 x+2),



since

Huh, Perito, you missed on thing there.

The derivative of ln (9x+2) is 9/(9x+2)

Ok, I'll post the general way to differenciate those types of equations:

For your derivative will be when e is exponential.

For your derivative will be when ln is any logarithm (ie ln and log)

EDIT::: Corrected the Sorry, was tired... with that MUN... rahhhh!

If y = ln [f(x)], then, dy/dx = f'(x)/f(x) where

but if y = log_3 [f(x)] then dy/dx = [ f'(x)/f(x) ] ln(3). Where log_3 is log to base 3.

Double post? How did I do that?

Oops. I thought correctly, I just wrote it wrong.

I did have



;)

Quote:

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Find equation of the straight line tangent to the following curve at the point where x = 1. (Round all coefficients to two decimal places.) Use graphing technology to check your answer by plotting the given curve together with the tangent line.
y = ln sqrt(5 x^2+6)

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Find the derivative of the given function and plug in x=1 to find the slope, m.

Plug in x=1 into the function as it is to find y. You are given x=1.

Plug all those into y=mx+b and solve for b. You're done.

To find the derivative of , use the chain rule.

Rewrite as using the log laws.

The derivative of the inside is

Since the derivative of ln(x) = 1/x, then we have

Multiply them:



The worst part is over... finish up?