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Integrate a^x with respect to x

This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a) exp(xln(a))=ln(a)a^x. By differentiatin...
JW
Answered by John W. • Maths tutor
41197 Views

Prove that √2 is irrational

Prove by contradiction: Assume negation to be true i.e. √2 is rational Then √2 can be written in the form a/b where a and b are integers with no common factor (the fraction cannot be simplified) => a/b = ...
PM
Answered by Paul M. • Maths tutor
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For y = 7x - x^3, find the two stationary points and what type of stationary points they are.

Differentiate y to get: dy/dx = 7-3x^2 , dy/dx = 0 , therefore x=(+/-)sqrt(7/3) d^2y/dx^2 = 6x , substitute x values in to y=7x-x^3 and d^2y/dx^2 to find coordinates and the type of the stationary point.
RS
Answered by Robbie S. • Maths tutor
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Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.

The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now set d...
JS
Answered by Joseph S. • Maths tutor
7719 Views

The line AB has equation 5x + 3y + 3 = 0. The line AB is parallel to the line with the equation y = mx + c. Find the value of m.

I like to separate problems into small steps that are easy to follow. In this example these would be: STEP 1: make y the subject (meaning only y on the Left hand side - LHS); 3y = -5x - 3. STEP 2: divide by ...
HS
Answered by Harrison S. • Maths tutor
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