If f(x)=x3+3x+4 and g is the inverse of f, then the value of 9|ddx(g(x)g(g(x)))| at x=4 is equal to

# If $f\left(x\right)={x}^{3}+3x+4$ and g is the inverse of f, then the value of  is equal to

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

$f\left(g\left(x\right)\right)=x⇒{f}^{\prime }\left(g\left(x\right)\right){g}^{\prime }\left(x\right)=1$

$\frac{d}{dx}\left(\frac{g\left(x\right)}{g\left(g\left(x\right)\right)}\right)=\frac{g\left(g\left(x\right)\right){g}^{\prime }\left(x\right)-{g}^{\prime }\left(g\left(x\right)\right){g}^{\prime }\left(x\right)g\left(x\right)}{\left(g\left(g\left(x\right)\right){\right)}^{2}}$

Also,

${f}^{\prime }\left(x\right)=3{x}^{2}+3⇒{f}^{\prime }\left(0\right)=3,g\left(g\left(4\right)\right)=g\left(0\right)=-1$

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)