$$\text { Find the formula for } d f ^ { - 1 } / d x \text {. }$$
-$$f ( x ) = x ^ { 11 / 5 }$$
A) $\frac { 11 } { 5 } x ^ { 6 / 5 }$
B) $\frac { 5 } { 11 } x ^ { - 6 / 11 }$
C) $x ^ { 6 / 11 }$
D) $x ^ { 5 / 11 }$

Question

Quizplus · Accepted Answer

To find the formula for $df^{-1}/dx$, we can use the chain rule: $$\frac{df^{-1}}{dx}=\frac{1}{\frac{df}{dx}}$$ First, we find $\frac{df}{dx}$: $$\frac{df}{dx}=\frac{11}{5}x^{11/5-1}=\frac{11}{5}x^{6/5}$$ Then, taking the reciprocal gives us: $$\frac{df^{-1}}{dx}=\frac{1}{\frac{df}{dx}}=\frac{5}{11}x^{-6/11}$$ Therefore, the answer is B.

Find the formula for df−1/dx. \text { Find the formula for } d f ^ { - 1 } / d x \text {. } Find the formula for df−1/dx.

$\text { Find the formula for } d f ^ { - 1 } / d x \text {. }$