Question

Find the derivative of the function z = 3t^17/3 − 2t^9/4 − t^1/2 + 8

Answer 1

Answer:

$\frac{-9x^{\frac{7}{4}}-1+34x^{\frac{31}{6}}}{2x^{\frac{1}{2}}}$

Step-by-step explanation:

first: we apply the sum-difference rule = $\frac{d}{dx}\left(3x^{\frac{17}{3}}\right)-\frac{d}{dx}\left(2x^{\frac{9}{4}}\right)-\frac{d}{dx}\left(x^{\frac{1}{2}}\right)+\frac{d}{dx}\left(8\right)$

solve $\frac{d}{dx}\left(3x^{\frac{17}{3}}\right)$ = $(\frac{17}{3})(3^(\frac{17}{3}-1)$ = $17x^ \frac{14}{3}$

solve $\frac{d}{dx}\left(2x^{\frac{9}{4}}\right)$ = $(\frac{9}{4})(2x^\frac{9}{4}^-^1)$ = $\frac{9}{2}x^(\frac{5}{4})$

solve $\frac{d}{dx}\left(x^{\frac{1}{2}}\right)$ = $\frac{1}{2\sqrt{x} }$

solve $\frac{d}{dx}\left(8\right)$ = 0

combine the answers: $= 17x^{\frac{14}{3}}-\frac{9x^{\frac{5}{4}}}{2}-\frac{1}{2x^{\frac{1}{2}}}+0$

simplify: $\frac{-9x^{\frac{7}{4}}-1+34x^{\frac{31}{6}}}{2x^{\frac{1}{2}}}$