Question

differentiate the function. y=(2x^4 - x + 1)(-x^5 + 7) y=□

Explanation:

Step1: Apply product - rule

$(uv)' = u'v+uv'$, where $u = 2x^{4}-x + 1$ and $v=-x^{5}+7$.

Step2: Differentiate $u$ and $v$

$u'=8x^{3}-1$, $v'=-5x^{4}$.

Step3: Substitute into product - rule

$y'=(8x^{3}-1)(-x^{5}+7)+(2x^{4}-x + 1)(-5x^{4})$.

Step4: Expand

$y'=-8x^{8}+56x^{3}+x^{5}-7-10x^{8}+5x^{5}-5x^{4}$.

Step5: Combine like - terms

$y'=-18x^{8}+6x^{5}-5x^{4}+56x^{3}-7$.

Answer:

$-18x^{8}+6x^{5}-5x^{4}+56x^{3}-7$