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# Differentiation Formulas

In the previous article, We learn about differentiation, Below are the list of different differentiation formulas:

## Differentiation Formulas

### 1. Differentiation Formulas for Trigonometric Functions

Trigonometry is the notion of the relationship among angles and sides of triangles. In the article, we have learned the main six ratios, such as sin, cos, tan, cot, sec, and cosec.  Here are the list of differentiation formulas for trigonometric function!!

1. $$\frac{d}{dx} (sin~ x)= cos\ x$$
2. $$\frac{d}{dx} (cos~ x)= – sin\ x$$
3. $$\frac{d}{dx} (tan ~x)= sec^{2} x$$
4. $$\frac{d}{dx} (cot~ x = -cosec^{2} x$$
5. $$\frac{d}{dx} (sec~ x) = sec\ x\ tan\ x$$
6. $$\frac{d}{dx} (cosec ~x)= -cosec\ x\ cot\ x$$
7. $$\frac{d}{dx} (sinh~ x)= cosh\ x$$
8. $$\frac{d}{dx} (cosh~ x) = sinh\ x$$
9. $$\frac{d}{dx} (tanh ~x)= sech^{2} x$$
10. $$\frac{d}{dx} (coth~ x)=-cosech^{2} x$$
11. $$\frac{d}{dx} (sech~ x)= -sech\ x\ tanh\ x$$
12. $$\frac{d}{dx} (cosech~ x ) = -cosech\ x\ coth\ x$$

There are given below differentiation formulas for trigonometric functions chart!!

### 2. Differentiation Formulas for Inverse Trigonometric Functions

Here are the list given below of differentiation formulas for inverse trigonometric functions

1. $$\frac{d}{dx}(sin^{-1}~ x)$$ = $$\frac{1}{\sqrt{1 – x^2}}$$
2. $$\frac{d}{dx}(cos^{-1}~ x)$$ = $$-\frac{1}{\sqrt{1 – x^2}}$$
3. $$\frac{d}{dx}(tan^{-1}~ x)$$ = $$\frac{1}{1 + x^2}$$
4. $$\frac{d}{dx}(cot^{-1}~ x)$$ = $$-\frac{1}{1 + x^2}$$
5. $$\frac{d}{dx}(sec^{-1} ~x)$$= $$\frac{1}{|x|\sqrt{x^2 – 1}}$$
6. $$\frac{d}{dx}(cosec^{-1}~x)$$= $$-\frac{1}{|x|\sqrt{x^2 – 1}}$$

These are the differentiation formulas for inverse trigonometric functions chart

### Other  Differentiation Formulas

Here are some other  differentiation formulas list!!

1. $$\frac{d}{dx}(a^{x}) = a^{x} ln a$$
2. $$\frac{d}{dx}(e^{x}) = e^{x}$$
3. $$\frac{d}{dx}(log_a~ x)$$ = $$\frac{1}{(ln~ a)x}$$
4. $$\frac{d}{dx}(ln~ x) = 1/x$$
5. Chain Rule: $$\frac{dy}{dx}$$ = $$\frac{dy}{du} × \frac{du}{dx}$$ = $$\frac{dy}{dv} × \frac{dv}{du} × \frac{du}{dx}$$

These are the other  differentiation formulas chart

## Types of Differential Equation

Differential equations can be classified into different types which name are —

• Ordinary Differential Equations
• Linear Differential Equations
• Non-linear differential equations
• Homogeneous Differential Equations
• Non-homogenous Differential Equations
• Partial Differential Equations
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