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Find the coordinates of the minimum point of the curve y = 3x^(2) + 9x + 10

(Note: in this answer I will use the notation y' to represent the differential of y, and by the same reasoning y'' denotes the differential of y', or the second derivative of y.) A curve's maximum or minimum...
JF
Answered by James F. • Maths tutor
27876 Views

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

Y=(2x-3)/x 2 Quotient Rule: dY/dx(u/v)=(u'v-v'u)/v 2 dY/dx=(2x 2 -2x(2x-3))/x 4 =(6x-2x 2 )/x 4 (Collect numerator x terms.) =(6-2x)/x 3 (Cancel the fraction by a factor of x.) dY/dx=(6-2x)/x 3
JD
Answered by Joe D. • Maths tutor
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[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 -x ​) - 4 * 1/2 (e x - e -x ) = 7Multiply by 2: 3 * (e x...
WU
Answered by William U. • Maths tutor
21880 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 f '(x) = [ 1 * (x-...
CB
Answered by Cosmin B. • Maths tutor
5582 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 following method: We choose eit...
CB
Answered by Cosmin B. • Maths tutor
5914 Views