Question

differentiate the function.
y = (3x^4 - x + 1)(-x^5 + 6)
y = □

Explanation:

Step1: Apply product - rule

$(uv)^\prime = u^\prime v+uv^\prime$, where $u = 3x^{4}-x + 1$, $v=-x^{5}+6$.

Step2: Differentiate $u$ and $v$

$u^\prime=12x^{3}-1$, $v^\prime=-5x^{4}$.

Step3: Substitute into product - rule

$y^\prime=(12x^{3}-1)(-x^{5}+6)+(3x^{4}-x + 1)(-5x^{4})$.

Step4: Expand

$y^\prime=-12x^{8}+72x^{3}+x^{5}-6-15x^{8}+5x^{5}-5x^{4}$.

Step5: Combine like - terms

$y^\prime=-27x^{8}+6x^{5}-5x^{4}+72x^{3}-6$.

Answer:

$-27x^{8}+6x^{5}-5x^{4}+72x^{3}-6$