Question

Consider the following. f(x) = 6x^{4} − 6x^{3} Find the following derivatives. f'(x)= f''(x)= f'''(x)=

Derivatives
ANSWERED
asked 2021-05-17
Consider the following.
\(\displaystyle{f{{\left({x}\right)}}}={6}{x}^{{{4}}}−{6}{x}^{{{3}}}\)
Find the following derivatives.
f'(x)=
f''(x)=
f'''(x)=

Expert Answers (1)

2021-05-18
Step 1
From the given data:
Step 2
\(\displaystyle{f{{\left({x}\right)}}}={6}{x}^{{{4}}}−{6}{x}^{{{3}}}\)
Now, differentiating the above equation with respect to x
\(\displaystyle{f}'{\left({x}\right)}={24}{x}^{{{3}}}-{18}{x}^{{{2}}}\)
Now, differentiating the above equation with respect to x
\(\displaystyle{f}{''}{\left({x}\right)}={72}{x}^{{{2}}}-{36}{x}\)
Now, differentiating the above equation with respect to x
f'''(x)=144x-36
12
 
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