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Differentiate y=x(e^x)

Write as y=uv u=x v=e x du/dx=1 dv/dx=e x Using the product rule, dy/dx=v du/dx + u dv/dx So dy/dx=e x (1)+x(e x )=e x (1+x)
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Answered by Isabel R. • Maths tutor
5383 Views

How do I find the roots and and coordinates of the vertex of the graph y = 2x^2 + 4x - 8 ?

y = 2x^2 + 4x - 8y = 2( x^2 + 2x - 4)Completing the square:y = 2( (x+1)^2 - 1 - 4 )y = 2(x+1)^2 -10the vertex of graph lies at the minimum value of y, and this occurs when x = -1:y = 2(-1+1)^2 -10y = -10ther...
JA
Answered by Joe A. • Maths tutor
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Solve the equation 3^(5x-2)=4^(6-x), and show that the solution can be written in the form log10(a)/log10(b).

So we have the equation initially in the form 3^(5x-2)=4^(6-x), and as the solution involves log10, then a sensible first move would be to take log10 of both sides, giving log10(3^(5x-2)) = log10(4^(6-x)). U...
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Answered by Eloise B. • Maths tutor
6616 Views

Prove that (sinx + cosx)^2 = 1 + 2sinxcosx

Starting on the left hand side we can expand out the brackets to get: (sinx + cosx)(sinx + cosx) sin 2 x+sinxcosx+sinxcosx+cos 2 x Grouping together the like terms we can rearrange it to be: sin 2 x + cos 2 ...
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Answered by Adam G. • Maths tutor
12649 Views

How do you integrate ln(x)?

Tricky. Definitely can't do it by inspection (we don't know any fuction that just differentaties to ln(x)), it's not like we've really got anything to substitute u for if we wanted to do it by substitution a...
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Answered by Ross G. • Maths tutor
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