# Thread: Differentiate by definition - please help

1. ## Differentiate by definition - please help

Can someone confirm I have done this correctly?

Y = 3x^4 + 2x^3 + 4x at P (x, y), let Q (X + Δx, y+Δy)
lim(Δx->0)
3(x+Δx)^4 + 2(x+Δx)^3 + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
Δx=lim(Δx->0)
3(x^4 + 4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(x^3 + 3x^2Δx + 3xΔx^2 + Δx^3) + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
Δx= lim(Δx->0)
3(4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(3x^2Δx + 3xΔx^2 + Δx^3) + 4(Δx)
lim(Δx->0) 3(4x^3+ 6x^2Δx + 4xΔx^2) + 2(3x^2 + 3xΔx + Δx^2) + 4(1)
3(4x^3) + 2(3x^2) + 4(1)

2. ## Re: Differentiate by definition - please help

Originally Posted by calcnewby
Can someone confirm I have done this correctly?

Y = 3x^4 + 2x^3 + 4x at P (x, y), let Q (X + Δx, y+Δy)
lim(Δx->0)
3(x+Δx)^4 + 2(x+Δx)^3 + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
Δx=lim(Δx->0)
3(x^4 + 4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(x^3 + 3x^2Δx + 3xΔx^2 + Δx^3) + 4(x+Δx) - (3x^4 + 2x^3 + 4x)
Δx= lim(Δx->0)
3(4x^3Δx + 6x^2Δx^2 + 4xΔx^3) + 2(3x^2Δx + 3xΔx^2 + Δx^3) + 4(Δx)
lim(Δx->0) 3(4x^3+ 6x^2Δx + 4xΔx^2) + 2(3x^2 + 3xΔx + Δx^2) + 4(1)
3(4x^3) + 2(3x^2) + 4(1)

I already gave you the answer,, forgot to mention it was in the wrong thread:

The answer is correct and we check it by taking the derivative:

$\frac{dy}{dx}= 4*3x^{3}+3*2x^{2}+ 4*1$

3. ## Re: Differentiate by definition - please help

Thanks for your help. I realized I had accidentally posted it in the wrong place so re-posted it before I realized you had already answered.