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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' = 6x sin(2x). uv' = 6x^2 cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [...
KS
Answered by Kilian S. • Maths tutor
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Solve algebraically the simultaneous equations: x^2+y^2 = 25 and y-3x=13

To answer this question, we need to make y the subject of the second equation. We can do this through simple rearrangement: y-3x=13 so y=13+3x Now that we have y on its own, this means we can substitute for ...
JK
Answered by James K. • Maths tutor
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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
TW
Answered by Thomas W. • Maths tutor
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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 from the va...
RS
Answered by Rajan S. • Maths tutor
6409 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 differentiating V = 4/3...
MA
Answered by Max A. • Maths tutor
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