Question

hw 12 - higher order derivatives section 2.7: problem 2 (1 point) calculate the second and third derivatives. $y = 5x^{4}-5x^{2}+3x$ $y=square$ $y=square$ note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have 6 attempts remaining. email instructor

Explanation:

Step1: Find the first - derivative

Use the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. For $y = 5x^{4}-5x^{2}+3x$, $y'=5\times4x^{3}-5\times2x + 3=20x^{3}-10x + 3$.

Step2: Find the second - derivative

Differentiate $y'$ with the power rule. $y''=\frac{d}{dx}(20x^{3}-10x + 3)=20\times3x^{2}-10=60x^{2}-10$.

Step3: Find the third - derivative

Differentiate $y''$ with the power rule. $y'''=\frac{d}{dx}(60x^{2}-10)=60\times2x=120x$.

Answer:

$y'' = 60x^{2}-10$
$y''' = 120x$