standard derivatives & formula method

STANDARD DERIVATIVES & formula method

Here is a revision of the standard derivatives which you have no doubt used many times before..

Copy out the list into a book and memorize those which you are not familiar with.

 

Y=f(x)	.dy/dx
1. Xn	NXn-1
2. ex	ex
3. ekx	kekx
4. ax	ax . lna
5. lnx	1/x
6. logax	1/x.lna
7. sin x	Cos x
8. cos x	-sin x
9. tan x	Sec2 x
10. cot x	-cosec2 x
11. sec x	Sec x. tan x
12. cosec x	-cosec x. cot x
13. sinh x	Cosh x
14. cosh x	Sinh x

We shall proceed with differentiation using the first derivative which is

Y= Xⁿ

^dy/dx= NX^n-1

(Known as formula method)

Where

X variable

N power

 

NOTE

When ever you wants to differentiate you will minus 1 (one) from the power and also multiply the power with the constant

 

e.g if you are asked to differentiate. x²

What you will do is this

Take the power back to multiply the constant associated with x, the minus 1 from the power

MATHEMATICALLY

.y = x²

.dy/dx = 2x^2-1

Therefore dy/dx = 2x^1. Which is 2x.

Now let’s proceed with other examples

Examples

1.    find f(x) = x²⁷

 

Solution

.dy/dx = 27x^27-1

.dy/dx = 27x²⁶ans

 

2.    differentiate with respect to x:f(x) = (8x³ + x² )

Solution

We shall differentiate this one after other

.dy/dx = 3*8x^3-1 + 2x^2-1

.dy/dx = 24x² + 2x

3.    find f(x) = x³ⁿ

Solution

.dy/dx = 3nx^3n-1 (using same procedure)

 

4.    find f(x) = (3x+4)

Solution

.dy/dx = 3 (note whenever you differentiate a constant it becomes zero)

 

5.    find f(x) = x ⁿ

solution

.dy/dx = nx ^n-1

 

at this juncture you can differentiate using formula method

we shall therefore move to more explicit ones

 

Exercises

Differentiate the following with respect to

1.    6x⁵ – 3x⁴ – 2x³

2.    7x⁴ – 5x³

3.    ax³ + bx

 

please try the exercises, it will make you more perfect, also try to read other math text book, if you encounter any challenges jus drop it here so that we can help you out.