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Differentiate sin(x)*x^2

Notice that (sin(x))'= cos(x) and (x^2)' = 2x We use the product rule to differentiate, by noticing the expression is a product. so (fx gx)' = f'x gx + fx*g'x substituting in we get (sin(x)*x^2) = cos(x)*x^2...
DG
Answered by Drenusha G. • Maths tutor
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Find the point of intersection of the lines y=2x-7 and 4y-2=3x

Substitute y into 4y-2=3x 4(2x-7)-2=3x -> 8x-28-2=3x -> 8x-3x=28+2 -> 5x=30 -> x=30/5 -> x=6 subsitute x into y=2x-7 y=2(6)-7 -> y=12-7 -> y=5 Point = ( 6 , 5 )
IG
Answered by India G. • Maths tutor
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Differentiate y=(3+sin(2x))/(2+cos(2x))

dy/dx = (4cos(2x) + 6sin(2x) + 2)/(2+cos(2x)) 2
MB
Answered by Matthew B. • Maths tutor
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Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x)) -1 . Next, find dy/dx in terms of cos(x) and sin(x). Again, we are f...
NL
Answered by Noah L. • Maths tutor
17937 Views

Solve the inequality x^2 > 3(x + 6)

In order to solve this inequality, it is helpful to have all the terms on the left-hand side of the equation. To do this, we can subtract 3(x + 6) from both sides of the equation. This gives us: x^2 - 3(x+6)...
JM
Answered by Joseph M. • Maths tutor
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