Top answers

Integrate: xe^x

Integrate by parts once to obtain: xe^x - e^x + c
DN
Answered by Daniel N. • Maths tutor
4054 Views

Given y = x(3x+ 5)^3. Find dy/dx.

First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our funct...
MS
Answered by Michael S. • Maths tutor
4936 Views

A curve C has equation y = x^2 − 2x − 24x^(1/2) x > 0 find dy/dx

dy/dx = 2x -2 -12x^(-1/2)
AS
Answered by Arshia S. • Maths tutor
7168 Views

Find the minimum value of the function, f(x)= x^2 + 5x + 2, where x belongs to the set of Real numbers

We first differentiate f(x), and we get f'(x)=2x + 5. We then set this equal to 0 and then solve for x. We get that xmin= -2.5. We check whether this was indeed a minimum, by calculating the second derivativ...
PP
Answered by Pavlos P. • Maths tutor
3903 Views

Find the gradient at the point (0, ln 2) on the curve with equation e^2y = 5 − e^−x . [4]

Figure out what skills are being tested: implicit differentiation and exponentials and logarithms.e 2y = 5 - e -x 2e 2y (dy/dx) = e -x (dy/dx) = e -x / 2e 2y At (0, ln2) (dy/dx) = e 0 / 2e 2ln2 e 2ln2 = 4 as...
TC
Answered by Theodore C. • Maths tutor
4411 Views