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Differentiate with respect to x, y = (x^3)*ln(2x)

By product rule, dy/dx = x 3 (2/2x) + 3x 2 ln(2x) = x 2 (1 + 3ln(2x))
TM
Answered by Thomas M. • Maths tutor
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a) Point A(6,7,2) lies on l1. Point B(9,16,5) also lies on l1. Find the distance between these two points. b) l2 lies in the same z plane as l1 and crosses l1 at A and is perpendicular to l1. Express l2 in vector form.

a) Distance between two points ((x2- x1)^2 + (y2-y1)^2)^1/2Substitute in values to find distance.b) Write out l1 in vector form using info from points A and B.Use knowledge of scalar product to construct l2'...
AN
Answered by Adam N. • Maths tutor
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express x^2-4x+9 in the form (x-q)^2+y

divide the coefficient of the x term by 2-4/2=-2this is the value of the term, q.to find the term, y, simply square the value of q, and subtract it from the number term, which is in this case, 9(-2)^2=4. y=9...
HC
Answered by Hugo C. • Maths tutor
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4. The curve C has equation 4x^2 – y3 – 4xy + 2y = 0. P has coordinates (–2, 4) lies on C. (a) Find the exact value of d d y x at the point P. (6) The normal to C at P meets the y-axis at the point A. (b) Find the y coordinate of A

Differentiate Implicitly with respect to x- ( do it term by term, terms with only x's diff normally, terms containing a Y should be differentiated following the standard pattern but then multiplied by dy/dx ...
HP
Answered by Hamish P. • Maths tutor
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A block of mass 5 kg is being pushed over level ground by rod at 60 degrees to horizontal with force 40 N with acc. 1.5 what is the frictional force of the surface and draw a diagram with the forces acting on the block

Block has normal force, weight, friction and the force from the rod acting on itResultant force = 5*1.5=7.5horizontal component of force from rod = 207.5= 20 - FF= 12.5
HB
Answered by Henry B. • Maths tutor
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