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differentiate with respect to x. i). x^(1/2) ln (3x),

From this we can see that equation has 2 parts therefore we should look to using the product rule which is used to differiantiate a two functions multiplied together so (fg)'=f'g+fg'. In this question the di...
JD
Answered by Jesse D. • Maths tutor
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Solve the quadratic equation, x^2 - 4x -5 = 0

Solve x 2 - 4x - 5 = 0 A very full explanation would be: Start by listing the pairs of numbers that can be multiplied together to get 1 * -5 = -5 (i.e. the coefficient of the first term multiplied by the las...
RH
Answered by Ryan H. • Maths tutor
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Solve for y and x, where x=y+1 and y=2x+3

Simultaneous equations: x=y+1 y=2x+3 First solve for x. y=2x+3 so first equation becomes: x=(2x+3)+1 x-2x-3-1=0 -1x-4=0x+4=0 x=-4 Solve for y: y=2x+3 y=2(-4)+3 y=-8+3y=-5
TS
Answered by Tom S. • Maths tutor
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Solve the simultaneous equations 2x + y = 7 and 3x - y = 8

There are three methods for solving simultaneous equations: elimination, substitution and by using graphs.Elimination is a good method in this case as the y terms are equal in both equations. We just add the...
TJ
Answered by Tia J. • Maths tutor
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Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).

Firstly, recall the definition of a logarithm: if y = log a (x), then this means that y is the power you have to raise a to, to get x, that is a y = x.Now, we want to introduce a new base, b. Let's take log ...
TH
Answered by Tom H. • Maths tutor
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