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