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Why is the derivative of x^2 equal to 2x?

The derivative tells us how much the output of a function changes when we change the input by a tiny amount. For the function f(x) = x 2 , we can think of the input as being a line of length x, and the outpu...
LI
Answered by Luke I. • Maths tutor
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A function is defined by f(x)= e^(x^2+4), all real x. Find inverse of f(x) and its domain.

Let f(x)=y: y = e^(x 2 +4); To find the inverse of a function, you need to find x in terms of y. In this case, you need to bring the exponent to the base. So in order to bring x 2 +4 from the power, take nat...
EC
Answered by Elisa C. • Maths tutor
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C is a circle with equation x^2 + y^2 = 16. The point P = (3,√7) is on C. Find the equation of the tangent to C at the point P.

First, we note the centre of the circle is at the origin (0,0). Then we calculate the gradient of the line OP, the line connecting the origin to P. The gradient = change in y / change in x = (√7 - 0) / (3 - ...
DC
Answered by Daniel C. • Maths tutor
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Solve sec(x)^2-2*tan(x)=4 for 0<=x<=360

We know sin(x)^2+cos(x)^2=1Dividing by cos(x)^2: tan(x)^2+1=sec(x)^2Substitute into the Equation and Rearrange to get: tan(x)^2-2*tan(x)-3=0Let y = tan(x): y^2-2y-3=0Factorising: (y-3)(y+1)=0so y = 3 and y =...
MR
Answered by Mukesh R. • Maths tutor
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y is inversely proportional to x. y = 0.04 when x = 80. Find the value of y when x = 32.

If y is inversely proportional to x. We know that y=k/x for some constant k. We need to find this constant before continuing. Looking at the information given to us in the question we know for one example th...
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Answered by Tyler T. • Maths tutor
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