Question

Differentiate the function: h(x) = 3/4 (x^5 – 4x^3 + 6)^8

Quadratic function and equation
ANSWERED
asked 2021-08-21
Differentiate the function:
\(\displaystyle{h}{\left({x}\right)}=\frac{{3}}{{4}}{\left({x}^{{5}}–{4}{x}^{{3}}+{6}\right)}^{{8}}\)

Expert Answers (1)

2021-08-22
Differentiate with respect to x. we get:
\(\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left\lbrace{h}{\left({x}\right)}\right\rbrace}=\frac{{3}}{{4}}\times{8}{\left({x}^{{5}}–{4}{x}^{{3}}+{6}\right)}^{{7}}\times{\left({5}{x}^{{4}}–{12}{x}^{{2}}+{0}\right)}=\)
\(\displaystyle={6}{\left({x}^{{5}}–{4}{x}+{6}\right)}^{{7}}{\left({5}{x}^{{4}}–{12}{x}^{{2}}\right)}={6}{x}^{{2}}{\left({5}{x}^{{2}}–{12}\right)}^{{7}}{\left({x}^{{5}}–{4}{x}^{{3}}+{6}\right)}\).
Therefore, \(\displaystyle{h}{\left({x}\right)}={6}{x}^{{2}}{\left({5}{x}^{{2}}–{12}\right)}{\left({x}^{{5}}–{4}{x}^{{3}}+{6}\right)}^{{7}}.\)
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