# What is the derivative of fog?

## What is the derivative of fog?

The function fog is called the composed function of g and f. If g is differentiable for any element x and f is differentiable at g(x) fog(x) = f[g(x)] is differentiable at x. The derivative of the function fog is (fog)'(x) = f”[g(x)].

**What does fog mean in math?**

Solution : f o g is a composite-function. f o g means g(x) function is in f(x) function. f o g = f[g(x)] f(x) = 2x -3 and g(x)= (x+3)/2. ∴ f[g(x)] =[2(x+3)/2] – 3.

### What is derivative of Arcsin?

Derivative of arcsin x Formula The derivative of the arcsin function is, d/dx(arcsin x) = 1/√1 – x² (OR) d/dx(sin-1x) = 1/√1 – x²

**How do you find inner and outer functions?**

For the function f(x) = e(x · cos(x)) , the outer function is f(x) = e(x) and the inner function is g(x) = x · cos(x).

## How do you find the composite function?

How to Solve Composite Functions?

- Write the composition in another form. The composition written in the form (f∘g)(x) ( f ∘ g ) ( x ) needs to be written as f(g(x)) f ( g ( x ) ) .
- For every occurrence of x in the outside function i.e. f , replace x with the inside function g(x) .
- Simplify the answer obtained.

**How to calculate derivative of FG with respect to X?**

If f(x) and g(x) are differentiable functions, then the derivative of the product fg with respect to x is given by (fg)’ = f ‘g + f g’ This can be fairly easily derived from the definition. Example To calculate the derivative of h(x) = x2exwe must use the product rule:

### Which is the derivative of the composition of G with F?

If f(x) and g(x) are differentiable functions, then the derivative of the composition of g with f is where the notation g'(f(x)) means the function g'(x) evaluated at f(x). Once again, this result can be established from the definition. Example

**What is the derivative of the function f ( x )?**

The derivative of a function is the ratio of the difference of function value f(x) at points x+Δx and x with Δx, when Δx is infinitesimally small. The derivative is the function slope or slope of the tangent line at point x.

## When is the derivative of g ( x ) not equal to zero?

If f(x) and g(x) are differentiable functions and g(x) is not equal to zero, then the derivative of the quotient f/gis which can be remembered with the saying “bottom-derivative-top minus top-derivative-bottom over bottom squared”.