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Differentiate (2x^2+5)^4 with respect to x

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Answer:

differentiate (2x+5)^2(x-4) u must know that it is a product function

Using the product rule you have dy/dx=udv/dx+vdu/dx

Let (2x+5)^2 be u and (x-4) be v

To find du we use chain rule which is du/dx=du/dw *dw/dx

We say let (2x+5) be w

We then have a new function like u=w^2

du/dw=2w

dw/dx=2

So du/dx=2*2w which equals 4w and w was (2x+5)

du/dx=4(2x+5)

dv/dx=1

So substitute everything into product rule we have

dy/dx=(2x+5)^2(1) + 4(2x+5)(x-4)

dy/dx=(4x^2 +20x+25) +(8x^2 -12x-80)

dy/dx=12x^2 +8x-55

dy/dx=(2x+5)(6x-11)

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