Chain Rule of Differentiation | Chain Rule of Derivatives

Quantitative Reasoning ( Q . R - I I )

The derivative of a function tells us the rate of change of one quantity with respect to another.
Mathematically, the derivative of a function
f ( x ) is written as:

f ' ( x ) = d / dx f ( x )

#whatisderivative
#definederivative
#rulesofderivative
#principlesofderivatives

1) d/dx ( c ) = 0

2) d/dx ( x ) = 1

3) d/dx ( cx ) = c

4) d/dx ( x^n) = n ( X ) ^ n - 1

5) d/dx { f(x) + g(x) } = f ' (x) + g ' (x)

6) d/ dx { f(x) g(x) } = f(x)g'(x) + g(x) f'(x)

7) d/ dx { U / V } = { U d/dx(V);- V d/dx(U) } / V^2

8) dy / dx = dy / du * du / dx
Simple Meaning

✓ It tells how fast a quantity changes.
✓ It also gives the slope of the tangent line to a curve at a point.

Applications

Derivatives are used to:
✓ Find maximum and minimum values
✓ Study motion (velocity and acceleration)
✓ Analyze growth and decay
✓ Solve problems in physics, economics, and engineering

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