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How do we differentiate y=a^x when 'a' is an non zero real number

Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.ln(y)=ln(a x ) ln(y)=x(ln(a)) using our rules of logsFrom here we differentiate. The differential...
MJ
Answered by Marcus J. • Maths tutor
8423 Views

If (m+8)(x^2)+m=7-8x has two real roots show that (m+9)(m-8)<0 where m is an arbitrary constant

For this we are going to test our knowledge of discriminats and factorisation. Firstly we will format the equation as (m+8)x 2 +8x+(m-7)=0From here we can see it takes the form ax 2 +bx+c, and as we know the...
MJ
Answered by Marcus J. • Maths tutor
5360 Views

Find the sum and product of the roots of the equation 2x^2+3x-5=0

We know that for equation ax^2+bx+c=0 a = 2,b = 3,c = -5 If the roots x1 and x2 are real numbers: x1 + x2 = -b/a = -3/2 x1*x2 = c/a = -5/2
PG
Answered by Pavel G. • Maths tutor
16659 Views

Find minimum and maximum of x^2+1 if they exist

There are several methods of finding the extrema(plural of extremums or in other words minimum or maximum values) of a function. For now we will analyse the function using the dy/dx of f(x)=y=x 2 +1, f ` (x)...
PG
Answered by Pavel G. • Maths tutor
5180 Views

Differentiate xcos(x) with respect to x

We have two functions multiplied together: x and cos(x). Therefore we have to use the product rule. First differentiate x and leave cos(x) untouched, so we get 1(cos(x))=cos(x). Then differentiate cos(x) and...
IL
Answered by Ioannis L. • Maths tutor
45698 Views