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Differentiate y=ln(2x^2) with respect to x

Making a substitution for u = 2x^2 Now y = ln(u) dy/dx = du/dx * dy/du du/dx = 4x dy/du = 1/u dy/dx = 4x/u Then substitute 2x^2 back in as u The final answer is 4x/(2x^2) Which can be simplified by dividing ...
CG
Answered by Catherine G. • Maths tutor
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If we have a vector 4x + 6y + z and another vector 3x +11y + 2z then what is the angle between the two?Give the answer in radians

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MS
Answered by Matthew S. • Maths tutor
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Express 3cos(x)+4sin(x) in the form Rsin(x+y) where you should explicitly determine R and y.

Since Rsin(x+y)=Rsin(x)cos(y)+Rsin(y)cos(x), we can set Rcos(y)=4 (1) and Rsin(y)=3 (2) on comparison to the desired equation. Considering (2) divided by (1) we see that tan(y)=sin(y)/cos(y)=3/4 so y=atan(3/...
WV
Answered by William V. • Maths tutor
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How Do I Integrate cos(x) and sin(x) with higher powers?

The answer to this question depends on one thing, whether this power is odd or even. For even powers we use the identity cos(2x) = 2cos^2(x)-1 = 1-2sin^2(x). So for example, the integral of cos^2(x) is found...
CR
Answered by Ciarán R. • Maths tutor
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differentiate: y^2 + 3xy + x + y = 8

dy/dx = 3x+1/ -2y-3x-1
GF
Answered by Gabrielle F. • Maths tutor
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