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Solve the equation 5^(2x) - 12(5^x) + 35 = 0

The first step to solving this is equation is to notice that the equation is of a similar to the form of a quadratic equation: ay^2 + by + c = 0 where a, b and c are constants. Next we introduce a new variab...
JG
Answered by Jacob G. • Maths tutor
11059 Views

Differentiate with respect to x: y = ln(x^2+4*x+2).

Let u = x 2 +4x+2 so y = ln(u). Then dy/du = 1/u and du/dx = 2x+4. Using the chain rule we have: dy/dx = (dy/du)*(du/dx) = (1/u)*(2x+4) = (2x+4)/(x 2 +4x+2).
OL
Answered by Okim L. • Maths tutor
5502 Views

Prove that sec^2(θ) + cosec^2(θ) = sec^2(θ) * cosec^2(θ)

These problems can be tricky as they use unfamiliar trigonometric functions such as secant and cosecant. It is much easier to approach these problems by replacing these trigonometric functions with more fami...
HR
Answered by Hugh R. • Maths tutor
12938 Views

find dy/dx at t, where t=2, x=t^3+t and y=t^2+1

We know from simple fraction rules that dy/dx=(dy/dt)/(dx/dt). dy/dt=2t, dx/dt=3t^2+1. Therefore, dy/dx=2x2/12+1=4/13
NO
Answered by Niamh O. • Maths tutor
6481 Views

A curve has equation x^2 + 2xy – 3y^2 + 16 = 0. Find the coordinates of the points on the curve where dy/dx =0

We would do this by differentiating everything individually so to differentiate x 2 we multiply the x 2 by the power which is 2 and then take the power down by 1 to make 2x. To differentiate 2xy we would use...
TK
Answered by Tom K. • Maths tutor
5476 Views