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Maths
A Level

Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6xsin(2x). uv' = 6x^2cos(2x), v^2 = 4cos^2(2x) Therefore the differe...

Answered by Kilian S. Maths tutor
5326 Views

Differentiate the function f(x)=2xsin3x

Use the product rule: u'v + uv' u = 2x     V= sin3x u'= 2       v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x

Answered by Thomas W. Maths tutor
4425 Views

differentiate the equation f(x) = 3x^2+5x+3

Look at each of the x variables to determine what happens to each term.

3x^2 has a power of 2 on the variable, therefore, the 2 is multiplied by the coefficient on the x. You must also subtract 1 f...

Answered by Rajan S. Maths tutor
5001 Views

A spherical balloon of radius r cm has volume Vcm^3 , where V =4/3 * pi * r^3. The balloon is inflated at a constant rate of 10 cm^3 s^-1 . Find the rate of increase of r when r = 8.

We are being asked to find the rate of change of radius, dr/dt. We will need to use the chain rule to do this: dV/dt = dV/dr * dr/dt.

We are given that dV/dt is 10cm^3 per second, and differentiati...

Answered by Max A. Maths tutor
12351 Views

Find the roots of y=x^{2}+2x+2

y=x2+2x-3

Can solve using quadratic equation. Using the square method to obtain for the square term and x term (x+1)(x+1) = x2+2x+1

Therefore (x+1)(x+1)-4=y

To f...

Answered by Harry S. Maths tutor
5472 Views

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