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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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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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(ii) Prove by induction that, for all positive integers n, f(n) = 3^(3n–2) + 2^(3n+1) is divisible by 19

Let P(n) represent the statement that 'f(n) is divisible by 19'. For the basis step, I prove that P(1) is true: f(1) = 3 3(1)-2 + 2 3(1)+1 = 19. 19 is divisible by 19 so P(1) is true. I now want to prove tha...
DL
Answered by Daniel L. • Maths tutor
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How do you find stationary points of an equation, eg. y=x^2+3x+2

Stationary points of an equation are found where the gradient of the tangent at this point equals zero. A diagram can illustrate this. To find them differentiate the given equation (which gives the gradient)...
EC
Answered by Ellie C. • Maths tutor
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Find the equation of the tangent to: y = X^2 + 3x + 2 at the point (2,12)

(1) Find the gradient using differentiation (2) If the gradient at (x 1 ,y 1 ) is m,y - y 1 = m(x - x 1 ) (1) We differentiate the given equation:dy/dx = 2x + 3 Then, find the gradient at (2,12). Sub x= 2 in...
SC
Answered by Samuel C. • Maths tutor
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