1. Tardigrade
  2. Question
  3. Mathematics
  4. Let h(x)=x g(x) where g is the inverse of f(x). Also the values of f(x) and f prime(x) are given as <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/mathematics/f031ce49c53c7788c4855338b925d145-.png /> then the value of h prime(5) equals

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $h(x)=x g(x)$ where $g$ is the inverse of $f(x)$. Also the values of $f(x)$ and $f^{\prime}(x)$ are given as
image
then the value of $h^{\prime}(5)$ equals

Continuity and Differentiability

Solution:

$h^{\prime}(5)=5 g^{\prime}(5)+g(5)=5 \cdot \frac{1}{f^{\prime}(3)}+g(5)=\frac{5}{2}+3=\frac{11}{2}$