Question

d/dx (x^2+7)^5 ( 2 +5x^2 -3x^3) i need full solution using product rule.
My answer is perhaps wrong.

Answer 1

what's your answer?

Answer 2

(x^2+7) (10+70x-42x^2-5x^3-9x^4) Checked using wolframalpha it is even more complex than the actual answer answer (x^2+7)^4 (90x-63x^2+60x^3-39x^4)

Answer 3

*(x^2+7)^4

Answer 4

Ok fine this involves Product rule and Product rule goes like
y = uv then, dy/dx = u* (dv/dx) + v*(du/dx)

ok so in this question we take
y = (x^2 + 7)^5 (2 + 5x^2 - 3x^3)
So our u = (x^2 + 7) ^ 5
and our v = (2 + 5x^2 - 3x^3)

using Product rule (that is uv = (u*( dv/dx) + v*(du/dx))
so our du/dx = 5(x^2 + 7)^4 * (2x) = 10x(x^2 + 7)^4
and our dv/dx = 10x - 9x^2

Substituting into product rule we have

(x^2 + 7)^5 (10x - 9x^2) + (2 + 5x^ 2 - 3x^3)(10x(x^2 +7)^4)
And i stop here :)