I am currently studying calculus on an open learning basis and was wondering if someone could take a look at these questions and answers I have posted and feed back on my method of working out etc. I am pretty sure these answers are correct but would appreciate any comments.

Question 1:

Obtain $\displaystyle \frac{dy}{dx}$ for the following expression.

$\displaystyle y=(5x + 4)^3$ so $\displaystyle 3(5x + 4)^2$ This is the 1st part.

I then differentiate the inner part of the function so:-

$\displaystyle (5x + 4)$ differentiates to 5. This is the the 2nd part.

I then multiply the 1st by the 2nd to get $\displaystyle 3(5x + 4)^2\times 5$

so $\displaystyle \frac{dy}{dx}=15(5x + 4)^2$

Question 2:

Obtain $\displaystyle \frac{dy}{dx}$ for the following expression.

$\displaystyle y=(3 - 2x)^5$ so $\displaystyle 5(3 - 2x)^4$ This is the 1st part.

I then differentiate the inner part of the function so:-

$\displaystyle (3 - 2x)$ differentiates to -2. This is the the 2nd part.

I then multiply the 1st by the 2nd to get $\displaystyle 5(3 - 2x)^4\times -2$

so $\displaystyle \frac{dy}{dx}=-10(3 - 2x)^4$

Question 3:

Obtain $\displaystyle \frac{dy}{dx}$ for the following expression.

$\displaystyle y=\sqrt{(5 - 0.6x)}$ which is $\displaystyle (5 - 0.6x)^\frac{1}{2}$

I then differentiate this to get $\displaystyle \frac{1}{2}(5 - 0.6x)^{-\frac{1}{2}}$ This is the 1st part:

$\displaystyle (5 - 0.6x)$ differentiates to -0.6. This is the the 2nd part.

I then multiply the 1st by the 2nd to get $\displaystyle \frac{1}{2}(5 - 0.6x)^{-\frac{1}{2}}\times -0.6$

so $\displaystyle \frac{dy}{dx}=-0.3(5 - 0.6x)^{-\frac{1}{2}}$

Question 4:

Obtain $\displaystyle \frac{dy}{dx}$ for the following expression.

$\displaystyle y=(2 + 3x)^-0.6$ so $\displaystyle -0.6(2 + 3x)^{-1.6}$ This is the 1st part.

I then differentiate the inner part of the function so:-

$\displaystyle (2 + 3x)$ differentiates to 3. This is the the 2nd part.

I then multiply the 1st by the 2nd to get $\displaystyle -0.6(2 + 3x)^{-1.6}\times 3$

so $\displaystyle \frac{dy}{dx}=-1.8(2 + 3x)^{-1.6}$

As I said at the beginning I am pretty sure I am 100% correct and I agree these are relatively simple questions from a calculus point of view but being new to this subject I was just wondering if someone could make comment please.

Thanks

Derek.