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Differentiate x^3⋅cos(5⋅x) with respect to x.

In order to solve this problem we will have to use the product rule as follows: d/dx[x^3⋅cos(5⋅x)]=[d/dx(x^3)]⋅cos(5x)+(x^3)⋅[d/dx[cos(5x)]]=(3⋅x^2)⋅cos(5⋅x)+(x^3)⋅−5⋅sin(5⋅x)=3⋅x^2⋅cos(5⋅x)−5⋅x...

Answered by Tianyu L. • Maths tutor

5672 Views

Work out 2 7/15 -1 2/3

First turn into improper fractions37/15 - 5/3Get same denominator on bottom37/15-25/15Take away numerator (37-25)/15= 12/15 Simplify 4/5

Answered by Henry G. • Maths tutor

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How would you factorise x^2 + 4x + 4

This is in the form ax² + bx + cWhere, a= 1b=4c=4To factor we have to find two numbers that:Add up to b, in this case 4Multiply together to give c

Answered by Toby B. • Maths tutor

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Points P and Q are situated at coordinates (5,2) and (-7,8) respectively. Find a) The coordinates of the midpoint M of the line PQ [2 marks] b) The equation of the normal of the line PQ passing through the midpoint M [3 marks]
a) For finding the midpoint M, the point M must be equidistant from P and Q in both the x and y axes. Hence, we consider the x and y axis separately. The midpoint of the x coordinates is essentially a mea...
JU
Answered by Justin U. • Maths tutor
3809 Views

The gradient of the curve at A is equal to the gradient of the curve at B. Given that point A has x coordinate 3, find the x coordinate of point B.
We are told f(x) = (2x-5)^2 (x+3).In part b) we are asked to show that f'(x) = 12x^2 -16x -35, so for part (c) we shall assume this definition for f'(x). We are told that the x coordinate for A is 3. Call...
TF
Answered by Thomas F. • Maths tutor
5867 Views

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Differentiate x^3⋅cos(5⋅x) with respect to x.

Work out 2 7/15 -1 2/3

How would you factorise x^2 + 4x + 4

Points P and Q are situated at coordinates (5,2) and (-7,8) respectively. Find a) The coordinates of the midpoint M of the line PQ [2 marks] b) The equation of the normal of the line PQ passing through the midpoint M [3 marks]

The gradient of the curve at A is equal to the gradient of the curve at B. Given that point A has x coordinate 3, find the x coordinate of point B.

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