Simple derivatives, Mathematics

Simple derivatives

Example   Differentiate following.

 (5x3  - 7 x + 1)5 ,[ f ( x )]5 ,[ y ( x )]5

Solution: Here , with the first function we're being asked to do the given,

d  [(5x3  - 7 x + 1)5/ dx =  5 (5x3  - 7 x + 1)4 (15x2  - 7 )

and it is just the chain rule.  We differentiated the outside function (the exponent of 5) and then multiplied that by the derivative of the inside function (the stuff inside the parenthesis).

For the second function we're going to do basically the similar thing.  We're going to have to use the chain rule. Still the outside function is the exponent of 5 whereas the inside function this time is simply f ( x ) . We don't contain a particular function here, however that doesn't mean that we can't at least write down the chain rule for this function. Following is the derivative for this function,

d  [ f ( x )]5 / dx = 5 [ f ( x )]4 f ′ ( x )

Actually we don't know what f ( x ) is so while we do the derivative of the inside function all we can do is write down notation for the derivative, that means f ′ ( x ) .

Along with the final function here simply we replaced the f in the second function along with a y since most of our work in this section will involve y's rather than f's.  Outside of that this function is alike to the second. Thus, the derivative is,

d  [ y ( x )]5  = 5 [ y ( x )]4  y′ ( x )

Posted Date: 4/12/2013 3:57:10 AM | Location : United States

Related Discussions:- Simple derivatives, Assignment Help, Ask Question on Simple derivatives, Get Answer, Expert's Help, Simple derivatives Discussions

Write discussion on Simple derivatives
Your posts are moderated
Related Questions
Spring, F s We are going to suppose that Hooke's Law will govern the force as the spring exerts on the object. This force will all the time be present suitably and is F s

How to Converting Percents to Fractions ? To convert a percent to a fraction: 1. Remove the percent sign. 2. Create a fraction, in which the resulting number from Step 1 is

If r,R denote position vectors of points on the straight lines in the direction of a and b respectively, and if n is a unit vector perpendicular to both these directions, show that

If depreciation/amortisation is done properly, impairment adjustments will not arise.   Required: Do you agree with the above statement? Critically and fully explain your

In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper. It is known that Theorem 3 on page 137 of the attached

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre. Since Δ ADF ≅ Δ DFC ∠ADF = ∠CDF ∴ ∠ADC = 2 ∠CDF

Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di

how to work out mode

Magnitude - Vector The magnitude, or length, of the vector v → = (a1, a2, a3) is given by, ||v → || = √(a 1 2 + a 2 2 + a 2 3 ) Example of Magnitude Illus