How do I differentiate y=(x+2) (x-1) (x+3)?
A good question indeed, I assume that you know the product rule for differentiation, in case you don’t, here’s a brief information about it.Lets assume two functions f(x) and g(x) whose derivatives exist.And their exists another function h(x), such that:h(x)=f(x).g(x)Now differentiating the equation wrt x, we’ll get:h’(x)= f’(x).g(x) + f(x).g’(x)So now coming to your question,y=(x+2).(x-1).(x+3)differentiating wrt xy’=(x+2)’.(x-1).(x+3)+(x+2).(x-1)’.(x+3)+(x+2).(x-1).(x+3)’y’=(x-1).(x+3)-(x+2)(x+3)+(x+2)(x-1)That’s it.
Differentiate: x(1+3x)^5?
Let u = x and v = (1 + 3x)^5 By the uv rule of differentiation, we have d(uv) = vdu + udv So, the derivative of x(1 + 3x)^5 is x * d((1 + 3x)^5)/dx + (1 + 3x)^5 * 1. = 3 * 5x * (1 + 3x)^4 + (1 + 3x)^5 = (1 + 3x)^4 * (15x + 1 + 3x) = (18x + 1)(1 + 3x)^4 Hope this helps.
How to differentiate (3x-5)^2?
y = (3x-5)^2 dy/dx = 2(3x - 5) d/dx 3 = 6(3x - 5) answer//
How to differentiate cos^2 3x?
..............2x - 5 f(x) = ln[-----------------] ..............cos^2(3x) ..............1....................cos... d/dx 2 - (2x - 5) d/dx 2cos(3x) d/dx - sin(3x) d/dx 3 f'(x) = ----------------- d/dx ----------------------------------------... ...........2x - 5.......................................... .......------------------- ..........cos^2(3x) from chain rule ...2cos^2(3x) + 6(2x - 5)cos(3x)sin(3x) =-------------------------------------... ............cos^4(3x) ...2cos(3x)[cos(3x) + 3(2x - 5)sin(3x)] =-------------------------------------... .............cos^4(3x) ......2[cos(3x) + 3(2x - 5)sin(3x)] =-------------------------------------... ...........cos^3(3x) ..........1...............2[cos(3x) + 3(2x - 5)sin(3x)] =------------------ x ----------------------------------------... .....2x - 5.........................cos^3(3x) ..----------------- .....cos^2(3x) ....cos^2(3x)..........2[cos(3x) + 3(2x - 5)sin(3x)] =--------------------- x ----------------------------------------... .....2x - 5.......................cos^3(3x) ...2[cos(3x) + 3(2x - 5)sin(3x)] =-------------------------------------... ..........(2x - 5)cos(3x) ....2cos(3x) + 6(2x - 5)sin(3x) =-------------------------------------... .........(2x - 5)cos(3x) ..... 6(2x - 5)tan(3x) + 2 =----------------------------------- answer// ............2x - 5