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y = x^3 ln x. Find dy/dx

dy/dx = u.dv/dx + v.du/dxu = x³, v = ln xdu/dx = 3x², dv/dx = 1/xdy/dx = 3x² lnx + x²

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A curve has equation y = 20x −x^2 −2x^3 . The curve has a stationary point at the point M where x = −2. Find the x-coordinate of the other stationary point of the curve.

dy/dx = 20 - 2x - 6x² = -6x² - 2x + 20 which factorises to dy/dx = (10 - 6x)(2 + x). This shows that x=-2 and x=10/6=5/3 are stationary points of y = 20x −x² −2x³

Answered by Xixi Y. • Maths tutor

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Find all values of x in the interval 0 ≤ x ≤ 2pi for 2sin(x)tan(x)=3

This questions involves the use of trigonometric identities, specifically [1] tan(x) = sin(x)/cos(x) and [2] sin²(x) + cos²(x) = 1.
Start by rearranging the given equations to ...

Answered by Jasmin C. • Maths tutor

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Find the derivative of sin(x)/x^3 with respect to x

First, bring the x to the numerator (top) as x^(-3). Then use the chain rule: State the first times derivative of the second plus state the second times the derivative of the first.State sin(x), then mult...

Answered by Tutor170145 D. • Maths tutor

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Which value of x gives the greatest value of "-x^2+8x-6"

There are 2 methods of solving this: completing the square or calculus, which makes this a versatile question for both GCSE and A Level students. It is also fairly simple to adapt.
Using calculus, th...

Answered by Tutor172970 D. • Maths tutor

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