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What is the point of a derivative?

A derivative is a rate of change. For example, let y equal some function of x. Then the derivative of y with respect to x is asking how much y changes with respect to x. We can show this for any x and if we ...
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Find the equation of the tangent line to the graph of y=2x^4-7x^3+x^2+3x when x=5

y=-13x+12
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Answered by Zyra A. • Maths tutor
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Find the differential of f(x)=y where y=3x^2+2x+4. Hence find the coordinates of the minimum point of f(x)

The differential of f( x ) is f'( x )=6 x +2 because we apply this basic formula: the differential of k x n = kn x n-1 where k is a constant.This is a positive quadratic, so it has a U shape that is above th...
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The variables x and y are related by y = 5^x. How do I find the value of x when y is set to 15?

15 = 5^x, we can easily solve this equation by using logs on either side which will give us: log15 = x log 5. Then by solving this for x, we get the result of 1.68 to two decimal places.
AB
Answered by Andrea B. • Maths tutor
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What is the differential of (14x^3-3x^2)^3

Chain Rule - Differential of the bracket x the initial power of the bracket x the initial bracket power-1 --- So Differential of bracket is 42x 2 - 6x--- Power of bracket is 3 ---Initial bracket power-1 is (...
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