# differentiation

1. ### a point of inflection

Question, I am learning how to sketch gradient function using the given features of the function y = f(x). The question in the book asked to sketch the gradient function of y=f(x) I was able to sketch it ( y=f'(x)), but the question got me thinking that if a y=f(x) has a point of inflection at...
2. ### Implicit Differentiation

y^2 = e^(xy) y' = ye^(xy) / [ 2y - xe^(xy) ] Is it wrong if my final answer written Like this? y = sqrt[ e^(xy) ] y' = ( sqrt[ e^(xy) ] )e^(xy) / [ 2( sqrt[ e^(xy) ] ) - xe^(xy) ]
3. ### What is the derivative of $x^{x^x}$?

What is the derivative of $x^{x^x}$?
4. ### Differentiation

Hi I'm struggling with some differentiation questions. Please could you show how to work these out as I've tried and tried and can't get to the right answer :( Differentiate with respect to x.... 1) cos(xy) - x = 2 2) x = tsinh(t) , y = cosh(t) 3) x = tan(t) , y = ln(cosh(tan(t))) 4)...
5. ### Find the Derivative

I have two questions. They are almost similar. I wanna know if their derivative will be same or different. (a) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx when x = -9. (b) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx.
6. ### Derivative of a Squared Root

y = [(x^2 + 1)^2]^(1/2) dy/dx = ?
7. ### Calculus - continuity and differentiation

Suppose f : R → R and g : R → R are differentiable, that f is odd and that g iseven. Use a special case of the result from the previous question to show that theirderivatives f′ and g′ are respectively even and odd. Deduce that g′(0) = 0. The bit from the previous question is that g′(x) = af...
8. ### Finding a smooth(infinitely differentiable) function

So I have to find a smooth (infinitely differentiable) function where a(t) = 1 if t<=0 and a(t) = 0 if t>=1, so the major thing is finding what a(t) is when 0<t<1, and I know it'll have something to do with e^(something) but I just can't seem to find it. Any help would be much appreciated!
9. ### Antidif and differentiation application!!!!!!!

Hi everyone, Find the equations of the tangents to the curve y = x^3 - 6x^2 + 12 +2 which are parallel to the line y = 3x. I have done other questions similar to this but they involve a point being given so it is possible to find the equation. So I attempted something but I dont think I'm on...
10. ### differentiation of multivariable

If w= 4x^2 +4y^2 +z^2 , x = (p sinØ cosθ ) , y = (p sinØ cosθ ) , z = (p cosØ), find ∂w / ∂θ , the ans given is 2p(3(sinØ)^2) + 1 ) , but my ans is different , is my ans wrong ?
11. ### Integrate dP/dt =kP

Integrate dP/dt = kP solving for P? And how do I find k if it is a constant?
12. ### Stuck on an Implicit Differentiation Problem

Hello. I'm teaching myself Calculus and have hit a road block at Implicit Differentiation. I understand it conceptually but one of the problems in the 30 year old calculus book (Thomas and Finney, if that rings any bells) that I got my hands on has me stumped. I'm trying to differentiate with...
13. ### Log Differentiation Proof

Here's my attempt at a problem. What do I do next... or do I need a totally different approach? Also, I tried to enter the question into the thread directly, but got an "invalid equation" when using TEX brackets. It worked on overleaf.com Why does it only appear to work here without the TEX...
14. ### differentiation

if y=1/X² , show that y d²y/dx² + (dy/dx)² -10y³=0 i cant solve this
15. ### implicit differentiation

to differentiate 5y(z^3)with respect to x , it should be -5y(3z^2)(dz/dx) - 5(dy/dx)(z^3) ?why the author only have -5y(3z^2)(dz/dx)
16. ### Solve the differential equation by integration

having some difficulty with this question help me please guys Solve the differential equation by integration: y' = y Solution is y = c ex but I dont understand it?
17. ### implicit partial differentiation

in the notes , 'by applying chain rule to LHS of the above equation ' , which eqaution is the author referring to ? it's given that f /x + (f/z)(z/x) = 0 , why not f /x + (f/z)(z/x) + (f/y)(y/x) = 0 ??? As we can see , the function contain variable x , y and z
18. ### differentiation equation

a particle of mass m is projected towards a point O with initial speed √5/3 m/s from a point P where [OP]=3 metres. the particle is repelled from O by a force of magnitude 4m/x³ where x is its distance from O.(i) show that the equation of motion is v dv=4x^-3 dx (ii) find how close the particle...
19. ### differentiation equation

a car starts from rest. when it is at a distance s from its starting point its speed is v and its acceleration is 25v+v³. show that dv=(25+v²)ds and find (correct to 2 decimal places) its speed when s=.01 this is how i went about it dv/dt= acceleration dv/dt=dv/ds×ds/dt=v×dv/ds v dv/ds=25v+v³...
20. ### integration and differentiation

given the differential equation dy/dx=y cosxfind the general solution given that y=2 when x= π /6 i cant solve this