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Use the quotient rule to differentiate: ln(3x)/(e^4x) with respect to x.

Quotient rule: d(u/v)/dx = [(du/dx)v-u(dv/dx)]/v^2
u = ln(3x)
v = e^4x
Find du/dx using chain rule:
u = ln(z) ==> du/dz = 1/z
z = 3x ==> dz/dx = 3
(du/dz)(dz/dx) = ...

Answered by Henry T. • Maths tutor
3735 Views

what is the largest stick can you fit into a cylinder, if the radius is 3cm and the length is 24cm. To 2d.p

If the radius is 3cm then the diameter is 6cm. the largest stick would be the hypotonuse between the length ans the base and therefore pythagoras is needed.Stick Length= sqrt(radius2+lenght

Answered by Elizabeth E. • Maths tutor
2487 Views

Solve the inequality x^2 – 5x – 14 > 0.

In order to solve this, the quadratic must be factorised. This means we're trying to get the equation into the form (x+a)(x+b)>0 where a and b are constants where a x b = -14 and a + b = -5. This turn...

Answered by Marcus P. • Maths tutor
9194 Views

A bag contains 8 oranges, 9 pears and 13 apples. What is the probability a pear is picked?

The probability of an event happening is defined as the number of outcomes you're looking for (in this example the number of pears, 9) divided by the total number of outcomes (i.e. the total number of fru...

Answered by Marcus P. • Maths tutor
2624 Views

Expand the following brackets: a) 4(x+3) b) 3(x-1)-2(x+5) c) (y-3)^2 d) (y-2)^2 + (y+3)^2

a) 4x + 12For this question you must expand out the bracket by multiplying the subjects within by the number at the front. 4x + (4 x 3) = 4x + 12
b) x - 13Although this question...

Answered by Jasmin F. • Maths tutor
4140 Views

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