Top answers

Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Step 1: We begin solving this problem by finding the gradient of the tangent line at H, which is equal to dy/dx. In this case, our curve has equations x = 3sinθ and y= 5cosθ. Now, we differentiate x and y wi...
PK
Answered by Pantelis K. • Maths tutor
9310 Views

Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions

Step 1: When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator. In our case we have that the power of quadratic equation in the nume...
PK
Answered by Pantelis K. • Maths tutor
19690 Views

A curve has equation y = 6ln(x) + x^2 -8x + 3. Find the exact values of the stationary points.

When thinking about stationary points, it is important to remember that these points happen when the gradient of the curve is 0 (-> dy/dx = 0), or if you prefer, when the rate of change of a graph is 0. S...
CP
Answered by Christopher P. • Maths tutor
7159 Views

Find dy/dx when y = x^2(cos(x)).

y = x 2 (cos(x)) therefore we will need to use the product rule, dy/dx = u dv/dx + v du/dx where u = x 2 and v = cos(x) du/dx = 2x and dv/dx = - sin(x), (don't forget the negative symbol when differentiating...
JS
Answered by Joseff S. • Maths tutor
33068 Views

If y = 5x^3 - 2x^2 + 2, what is dy/dx?

Differentiation can be done term-by-term, so we can treat the 5x 3 , -2x 2 and 2 separately. We can also 'take out' the coefficients: to differentiate 5x 3 , for example, differentiate x 3 first and then mul...
AK
Answered by Alex K. • Maths tutor
9809 Views