Answers>Maths>A Level>Article

A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

3x^4/3-16y^3/4=32Differentiating implicitly:4x^1/3-12y^-1/4(dy/dx)=0Simplifying and rearranging:x^1/3=3y^-1/4(dy/dx)dy/dx=1/3(x^1/3y^1/4)
Finding dy/dx using the (x,y) co-ordinates given:dy/dx=1/3(8^1/3)(1^1/4)=1/3(2)(1)=2/3

Answered by Ben G. • Maths tutor

3898 Views

See similar Maths A Level tutors

A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

Related Maths A Level answers

If a ball is dropped from 6m above the ground, how long does it take to hit the floor and what is its speed at impact (assuming air resistance is negligible)?

Differentiate x^(1/2)ln(3x) with respect to x.

Let X be a normally distributed random variable with mean 20 and standard deviation 6. Find: a) P(X < 27); and b) the value of x such that P(X < x) = 0.3015.

A curve C has equation: x^3+2xy-x-y^3-20=0. Find dy/dx in terms of x and y.