I have two hours to learn derivatives before a quiz I have in

>>35261585
Baimpuh

Derivatives were taught in HS

Get out

d/dx x^n=nx^(n-1)
d/dx f(g(x)) = g'(x) f'(g(x))
d/dx f(x) g(x) = f'(x) g(x) +f(x) g'(x)
d/dx exp(x) = exp(x)

Literally all you need.

>>35262517
Also
d/dx sin = cos
d/dx cos = - sin
d/dx log(x) = 1/x

Derivatives are the last easy babyshit chapter you have before your life becomes the ThinkGeek STEM major sociopath route

File: 20170303_101334.jpg (807KB, 3264x1836px) Image search: [Google]

807KB, 3264x1836px

>>35262517
Then how do u do this

File: 20170303_101715.jpg (734KB, 3264x1836px) Image search: [Google]

734KB, 3264x1836px

>>35262638
Better pic, dont know why its upsidediwn

>>35262638
u(x) = (2x+3)^2
v(x) = 1/sqrt(x) =x^-(1/2)

f(x) = u(x)*v(x)
Apply chain rule to each to get du/dx and dv/dx

Use product rule:
df/dx = u*dv/dx + v*du/dx

Alternatively you can use the quotient rule (a special case of product rule):

f(x) = u(x)/v(x); u(x) = (2x+3)^2, v(x) = sqrt(x)
(Notice the choice for v is different)

df/dx = (1/v^2)*(v*du/dx - u*dv/dx)

>>35262791
Yeah im fkd

>>35262720
nigga, its a fraction
rewrite as:

(2x+3)^2 * x^(-1/2)

use your general derivative rules to solve, isnt that hard. But yeah OP if you don't get that, you're fucked

>>35262720
These aren't numbers, what is this??

This is year 1 calculus. MAT136 where I'm from. Good luck. It gets 5 times as hard in the second half.

>>35262720
The easiest thing to do is to just do algebra to make it a sum of terms then use the power rule.

(2x+3)^2 = (2x+3)(2x+3) = 4x^2 + 12x + 9

Remember that sqrt(x) is the same thing as x^0.5 so it's easy to divide by it. Just subtract 0.5 from all the exponents of x. Remember that a term which doesn't have an x is like a term that has x^0, because x^0 =1.

4x^1.5 + 12x^0.5 + 9x^-0.5

Now do the power rule, which means you multiply the number by the power then subtract 1 from the power.

(4*1.5)x^0.5 + (12*0.5)x^-0.5 + (9*-0.5)*x^-1.5

6x^0.5 + 6x^-0.5 - 4.5x^-1.5

Does that make sense? You could use the chain rule or the quotient rule, but the chain rule can be complicated and the quotient rule is hard to remember for me. Other than the power rule, all you need to know is algebra.

>>35261585
So you happen to be in Elbilia or just Casa .

>>35263162
>>35263162
yeah, fuck the second half of year 1 calculus
differential equations are fucking stupid

>>35263315
what the fuck how did I fuck up the second spoiler jesus.