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Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2

First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is eq...

Answered by Bogdan-Adrian M. • Maths tutor

7317 Views

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.)

Answered by James F. • Maths tutor

26868 Views

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...
JD
Answered by Joe D. • Maths tutor
6251 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
WU
Answered by William U. • Maths tutor
21229 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
CB
Answered by Cosmin B. • Maths tutor
5055 Views
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Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2

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

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

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

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

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