Derivative of an undeveloped function
1. How do we differentiate an implicit function?
Solution:
Let an implicit function F[x; f(x)] = 0 be given. When differentiating it, differentiate the terms containing only x in the usual way; differentiate the terms with y as composite functions. Multiply their derivative (with respect to y) by y′. Solve the equation for y′.
For example:
2. Differentiate the function:
Solution:
3. Differentiate the function:
Solution:
4.Differentiate the function:
5.Under what angle do the curves x2 + y2 – 5 = 0 and y2 – 4x = 0 intersect?
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6.Differentiate the function x3 + y3 − 3axy = 0
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7.Differentiate the function ey + e–x + xy = 0
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8.Compute the first derivative of the function exy − x2 + y3 = 0 at x = 0
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9.Write the equation of the tangent to the circle x2 + y2 + 4x − 4y + 3 = 0 at the point where the circle intersects the x-axis.
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10.Write the equation of the tangent to the curve
