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).
3x4/3-16y3/4=32Differentiating implicitly:4x1/3-12y-1/4(dy/dx)=0Simplifying and rearranging:x1/3=3y-1/4(dy/dx)dy/dx=1/3(x1/3y1/4)
Finding dy/dx using the (x,y) co-ordinates given:dy/dx=1/3(81/3)(11/4)=1/3(2)(1)=2/3
BG
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How do I simply differentiate and what does a differential mean?