Question

find the indicated derivative for the function.
f(x) for f(x)=6x^7 - 6x^6 + 8x - 6
f(x)=\square

Explanation:

Step1: Find the first - derivative

Use the power rule \((x^n)^\prime=nx^{n - 1}\).
For \(y = 6x^{7}-6x^{6}+8x - 6\),
\(f^\prime(x)=\frac{d}{dx}(6x^{7})-\frac{d}{dx}(6x^{6})+\frac{d}{dx}(8x)-\frac{d}{dx}(6)\)
\(f^\prime(x)=6\times7x^{6}-6\times6x^{5}+8\times1-0\)
\(f^\prime(x)=42x^{6}-36x^{5}+8\)

Step2: Find the second - derivative

Differentiate \(f^\prime(x)=42x^{6}-36x^{5}+8\) with respect to \(x\) again.
\(f^{\prime\prime}(x)=\frac{d}{dx}(42x^{6})-\frac{d}{dx}(36x^{5})+\frac{d}{dx}(8)\)
Using the power rule \((x^n)^\prime=nx^{n - 1}\), we have \(f^{\prime\prime}(x)=42\times6x^{5}-36\times5x^{4}+0\)
\(f^{\prime\prime}(x)=252x^{5}-180x^{4}\)

Answer:

\(252x^{5}-180x^{4}\)