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Differentiate 3x^(2)+xy+y^(2)=12 with respect to x

this is implicit differentiation. We start by differentiating 3x^(2) to get 6x (lower the power by 1, multiply by the original power). For xy, we use the product rule, giving us y + (x)dy/dx (this is the imp...
NL
Answered by Noyonika L. • Maths tutor
4771 Views

How do I use the product rule for derivatives?

Imagine a function f(x)=g(x)*h(x) [that is, two functions multiplied together] To find the derivative, f'(x)=g'(x)*h(x) + g(x)*h'(x) For example, f(x) = (3x 2 )*(cos x ) [g(x)=3x 2 , h(x)=cosx] f'(x) = (6x) ...
JW
Answered by James W. • Maths tutor
4291 Views

Solve 3(3x - 2) = 5x + 10

9x - 6 = 5x + 10 9x - 6 - 5x = 5x + 10 - 5x 4x - 6 = 10 4x - 6 + 6 = 10 + 6 4x = 16 x = 16/4 = 4
SP
Answered by Suraj P. • Maths tutor
4954 Views

How can we calculate the sinus of 120°?

We can observe that120° represents the sum of two common angles: 30° and 90°. So we can rewrite sin(120°) as sin(30°+90°). Now we are going to use this trigonometric formula in order to calculate the sinuns:...
MM
Answered by Monica M. • Maths tutor
8355 Views

How would you go about integrating a function which has an exponential and a cos/sin term?

For this type of integral you would need to use integration by parts twice. Remember this is where the integral of u*(dv/dx)=uv-(integral with respect to x)(v*(du/dx)). For example let's say you need to inte...
LR
Answered by Luke R. • Maths tutor
4445 Views