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Find the tangent of the following curve, y=xe^x, at x=1 expressing it in the form y=mx+c?

Firstly, we calculate the y-value when x=1, namely y=e. Then we need to find the gradient of this curve at x=1, which can be determined by taking the derivative of y and then valuate it at x=1. So dy/dx=xe^x...
BS
Answered by Bruno S. • Maths tutor
18962 Views

given y=(1+x)^2, find dy/dx

There are two ways in which this we can do this, The first is explanding the brackets to get 1+2x+x 2 and differentiating to get 2+2x. The second way is using the chain rule , let u=1+x such that y=u 2 and d...
SG
Answered by Sam G. • Maths tutor
9260 Views

What is the product rule and when do you use it?

The product rule is used when finding the derivative of the product of two functions - two functions multipled together. If y = f(x)g(x), then dy/dx = f'(x)g(x) + f(x)g'(x) Where f'(x) is the derivative of f...
TJ
Answered by Tom J. • Maths tutor
5487 Views

How do you integrate the function cos^2(x)

At first, you might think that it is possible to perform this integral simply by inspection, using the 'backwards chain rule'. This method would consist of adding one to the power, to get cos 3 (x), then div...
ER
Answered by Edward R. • Maths tutor
8673 Views

What is the natural logarithm?

The standard rule for integration is: integrate kx^n dx = kx^(n+1)/(n+1). However, if we try and integrate 1/x in this manner we get, x^0/0, i.e. 1/0, which is infinity. However, if we look at a graph of 1/x...
EH
Answered by Eden H. • Maths tutor
5245 Views