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How do you find the gradient of a curve?

Unlike a straight line, the gradient of a curve is not a constant i.e. not one single number. To find the gradient of a curve, you different the equation of the curve. To find the gradient at a specific poin...
AM
Answered by Anna M. • Maths tutor
44071 Views

Use integration by parts to find the integral of sin(x)*exp(x)

First, we choose u=sin(x),v'=exp(x). Using differentiation and integration of standard exponential and trigonometric functions => u'=cos(x),v=exp(x). From this we use the formula for integration by parts ...
PL
Answered by Philip L. • Maths tutor
7693 Views

Differentiate, y = 2x^3 + 2/x + 3

Differentiate by multiply by the power and then minus 1 from the power. Use the rule: y= ax^b -> dy/dx = abx^(b-1) dy/dx = 3 x 2x^(3-1) + -1 x 2x^(-1-1) + 0 dy/dx = 6x^2 - 2x^-2
CH
Answered by Claudia H. • Maths tutor
4635 Views

How do you integrate ln(x)?

Use the method of integration by parts. uv-integral(v.du/dx). Make u equal to ln(x) and dv/dx equal to 1. Therefore v=x and du/dx=1/x. Hence uv=xln(x). And v.du/dx=x/x=1. Substituting these into the 'by part...
MS
Answered by Michael S. • Maths tutor
3662 Views

How do you differentiate y=sin(cos(x))?

To solve this question we will use the chain rule, as we can see that we have one function being applied to another, i.e sin is being applied to cos(x). This means we are able to replace the original functio...
MP
Answered by Marcel P. • Maths tutor
19125 Views