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Show that the derivative of ln(x) = 1/x

We can start by letting y = ln(x) What we are trying to show is that dy/dx = 1/x Since y = ln(x), then e y = e ln(x) = x Taking the derivative of each side of this equation will give us e y .dy/dx = 1 If we ...
JC
Answered by James C. • Maths tutor
11326 Views

Differentiate y = x^3 +x^2 - 4x +5 with respects to x.

When differentiating, you want to use the formula ax^n differentiates to (a n)x^(n-1), so for the example above, x^3 where a is 1, and n is 3, the differentiation is (1 3)x^(3-1) which results to 3x^2. This ...
MS
Answered by Manojhan S. • Maths tutor
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Solve the differential equation: e^(2y) * (dy/dx) + tan(x) = 0, given that y = 0 when x = 0. Give your answer in the form y = f(x).

This is a question taken from a core 4 paper and is a typical example of a differential equation question. The first thing to notice about this equation is that it is "separable", meaning we can re...
DD
Answered by Dominic D. • Maths tutor
12639 Views

Differentiate The Following function

Find dy/dx where y = (x 2 +7) 1/2 => 1/2(x 2 +7) -1/2 * d/dx(x 2 +7) By the chain rule => 1/2(x 2 +7) -1/2 * 2x => x(x 2 +7) -1/2 Remember that x 1/2 = sqrt(x) and x -1 = 1/x => x/sqrt(x 2 +7)
KM
Answered by Kerr M. • Maths tutor
7478 Views

What is the gradient of the function f(x) = 2x^2 + 3x - 7 at the point where x = -2?

To work out the gradient of a function f(x), we need to differentiate it with respect to x, to give us f'(x). If x = a at a point, then the gradient of f(x) at that point is f'(a) (substitute a in place of x...
JJ
Answered by Jake J. • Maths tutor
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