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differentiate ln( x^2 )

ln is the natural log. The thing to remember with differentiating natural log is the simple formula U'/U. The U is whatever is in the brackets. This means we differentiate X^2 and divide it by X^2. X^2 ...

Answered by Edward T. • Maths tutor

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Find dy/dx where y= x^3(sin(x))

To differentiate y, we must used the product rule.The product rule is d/dx [f(x)g(x)] = f'(x)g(x) + g'(x)f(x)So here, we let f(x)= x^3 and g(x)= sin(x)Then, f'(x)= 3x^2 and g'(x) = cos(x)Then substituting...

Answered by Kajal C. • Maths tutor

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Find dy/dx when y = x(4x + 1)^1/2

Here we can use the product rule where dy/dx = v du/dx + u dv/dx.We let u = x and v = (4x + 1)^1/2 which means we get du/dx = 1 and by using the chain rule we get dv/dx = 1/2(4x + 1)^-1/2

Answered by Rebecca N. • Maths tutor

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There are 11 pens in a bag, 4 Green and 7 Blue. What is the probability of picking the same coloured pens?

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Answered by Laura H. • Maths tutor

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Express '6cos(2x) +sin(x)' in terms of sin(x).

6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin...

Answered by Robbie M. • Maths tutor

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