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Given that x = ln(sec(2y)) find dy/dx

x = ln (sec (2y)) The chain rule states that d/dy f (g (y)) = f'(g(y)). g'(y) Here g(y) = sec(2y) so g'(y) = 2.sec(2y).tan(2y) And f(y) = ln (y) so f'(y) = 1 / y Thus dx/dy = (1 / sec(2y)) . (2.sec(2y).tan(2...
DH
Answered by Dom H. • Maths tutor
13581 Views

f(x) = x^3 + 3x^2 + 5. Find f''(x)

f''(x) means that we need to differentiate the function f(x) twice (f'(x) would mean we need to do it once). Differentiation means we multiply the coefficient by the power, and subtract one from the power. S...
FM
Answered by Felix M. • Maths tutor
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The line l1 has equation y = −2x + 3. The line l2 is perpendicular to l1 and passes through the point (5, 6). (a) Find an equation for l2 in the form ax + by + c = 0, where a, b and c are integers.

The first thing to look at is l2 and l1 being perpendicular. This means the gradients of the two lines multiplied together = -1 . To determine the gradient a student could differentiate l1 but a slightly qui...
RP
Answered by Roman Paul M. • Maths tutor
17590 Views

SOLVE THE FOLLOWING SIMULTANEOUS EQUATIONS: 5x^2 + 3x - 3y = 4, -4x - 6y + 5x^2 = -7

Question: 5x 2 + 3x - 3y = 4, -4x - 6y + 5x 2 = -7.........Step 1: make the y-coefficient equal in both equarions: (y and not x because it has the lowest power so it is easier, but x would also work)...........
AM
Answered by Alonso M. • Maths tutor
7218 Views

Use integration by parts to integrate ∫ xlnx dx

∫ u(dv/dx) dx = uv − ∫ v(du /dx)dx is the Integration by Parts formula. If you set u=lnx, differentiation (rememeber from tables) leads to du/dx= 1/x, and dv/dx=x and so v=x^2/2 (raise power by one then divi...
MM
Answered by Minty M. • Maths tutor
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