Given the derivative below find the requested higher-order derivative. $f ^ { tt } ( x ) = 8 x ^ { \frac { 7 } { 5 } } , f ^ { ( i v ) } ( x )$
A) $f ^ { ( i v ) } ( x ) = - ( 56 / 5 ) x ^ { 2 / 5 }$
B) $f ^ { ( i v ) } ( x ) = ( 112 / 25 ) x ^ { 2 / 5 }$
C)$f ^ { ( i v ) } ( x ) = ( 112 / 25 ) x ^ { \frac { - 3 } { 5 } }$
D) $f ^ { ( i v ) } ( x ) = ( 56 / 5 ) x ^ { 2 / 5 }$
E) $f ^ { ( i v ) } ( x ) = - ( 112 / 25 ) x ^ { \frac { - 3 } { 5 } }$

Question

Quizplus · Accepted Answer

To find the fourth derivative $f^{(iv)}(x)$ of the given function $f^{tt}(x) = 8x^{\frac{7}{5}}$, we differentiate step by step:1. Third derivative $f^{(iii)}(x)$: Differentiating $8x^{\frac{7}{5}}$ gives $\frac{56}{5}x^{\frac{2}{5}}$.2. Fourth derivative $f^{(iv)}(x)$: Differentiating $\frac{56}{5}x^{\frac{2}{5}}$ gives $\frac{112}{25}x^{\frac{-3}{5}}$.Thus, the correct answer is $f^{(iv)}(x) = \frac{112}{25}x^{\frac{-3}{5}}$.

Given the Derivative Below Find the Requested Higher-Order Derivative ftt(x)=8x75,f(iv)(x)f ^ { tt } ( x ) = 8 x ^ { \frac { 7 } { 5 } } , f ^ { ( i v ) } ( x )ftt(x)=8x57​,f(iv)(x)

Given the Derivative Below Find the Requested Higher-Order Derivative $f ^ { tt } ( x ) = 8 x ^ { \frac { 7 } { 5 } } , f ^ { ( i v ) } ( x )$