#### To determine

**To state:**

Differentiation rule in symbols and in words.

#### Explanation

**a)Power rule:**

Let fx=xn be power function where n is a positive integer. Then, derivative of f is,

f'x=ddxxn=n.xn-1

is called as power rule.

In Leibniz notation,

f'x=ddxxn=n.xn-1

**b)The constant multiple rule:**

The derivative of a constant times a function is the constant times the derivative of the function.That is;

If f is a differentiable function and c is a constant, then

cf'=cf'

In Leibniz notation,

ddxcfx=c.ddxf(x)

**c)The sum rule:**

The derivative of sum of functions is the sum of the derivatives.

If f and g are both differentiable, then

f+g'=f'+g'

In Leibniz notation,

ddxfx+gx=ddxfx+ddxg(x)

**d)Difference rule: **The derivative of difference of two functions is the difference of their derivatives

By writing f-g as f+(-1)g and applying the sum rule and the constant multiple rule,

If f and g are both differentiable, then

f-g'=f'-g'

In Leibniz notation,

ddxfx-gx=ddxfx-ddxg(x)

**e)The product rule**:

Derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

If f and g are both differentiable, then

f.g'=f.g'+g.f'

In Leibniz notation,

ddxfxgx=fx.ddxgx+gx.ddx[fx]

**f)The quotient rule:**

The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

If f and g are differentiable, then

fg'=gf'-fg'g2

In Leibniz notation,

ddxfxgx=gx.ddxfx-fx.ddx[gx]gx2

**g)The chain rule**:

If g is differentiable at x and f is differentiable at g(x), then the composite function F=fοg defined by F(x)=f(gx) is differentiable at x and F' is given by the product

F'x=f'gx.g'(x)

In Leibniz notation, if y=f(u) and u=g(x) are both differentiable functions, then

dydx=dydu.dudx

**Final statement:**

We were able to state the 7 differentiation rule in symbols and in words.