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Differentiate with respect to x and write in its simpliest form, Y=(2x-3)/x^2?

Y=(2x-3)/x²

Quotient Rule: dY/dx(u/v)=(u'v-v'u)/v²

dY/dx=(2x²-2x(2x-3))/x⁴

=(6x-2x²)/x⁴(C...

Answered by Joe D. • Maths tutor

5377 Views

[FP2] Solve: 3 cosh x - 4 sinh x = 7

First write cosh and sinh as exponentials, from their respective definitions:sinh x = 1/2 (e^x - e^-x)cosh x = 1/2 (e^x + e^-x)So: 3 * 1/2 (e^x + e

Answered by William U. • Maths tutor

19833 Views

How can we calculate the derivative of function f(x)= (x+2)/(x-1)?

In order to calculate the derivative of the given function, we need to apply the laws of derivation. Therefore:
f '(x) = ((x+2)/(x-1))'
f '(x) = [(x+2)' * (x-1) - (x+2) * (x-1)' ]/ (x-1)²

Answered by Cosmin B. • Maths tutor

4271 Views

How can we solve a two-equation, two-unknown values?

If we have two equations that look like this:
a1 * x + b1 * y = c1
and
a2 * x + b2 * y = c2
where x,y are variables and a1,a2,b1,b2 are coeficients.
then we solve it using the fol...

Answered by Cosmin B. • Maths tutor

4794 Views

∫ log(x) dx

Using "Integration by parts" or "reverse chain rule" .
Recall formula for intergration by parts: "∫f'(x) g(x) dx = f(x)g(x) - ∫f(x)g'(x)dx"
Then set f'(x) = 1, g(x)...

Answered by Michael T. • Maths tutor

47970 Views