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How do I find the derivative of 2^x?

To find the derivative of any number to the power "x", such as 2 x , 5 x , or even 4.13 x , we first consider the general form a x . We need to be a little creative here. We know that any variable ...
KS
Answered by Katerina S. • Maths tutor
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Given two functions f and g where f(x)=3x-5 and g(x)=x-2. Find: a) the inverse f^-1(x), b) given g^-1(x)=x+2, find (g^-1 o f)(x), c) given also that (f^-1 o g)(x)=(x+3)/3, solve (f^-1 o g)(x)=(g^-1 o f)(x)

a) For an inverse function- "inputs become outputs" so swap the positions of the input-variable (i.e "x") with the output variable (i.e f(x)) and then rearange. Once rearanged so that f(x...
KK
Answered by Kendra K. • Maths tutor
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Given that y = -16x2​​​​​​​ + 160x - 256, find the value of x giving the maximum value of y, and hence give this maximum value of y.

y = -16x 2 + 160x - 256 x = 5 y = 144
MC
Answered by Matthew C. • Maths tutor
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What is a derivative - Introduction to Calculus

Strictly speaking, the derivative is the rate of change of a function, process or pattern. So far, to calculate the gradient of a given function we always computed the change in the y coordinates divided by ...
GM
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In an arithmetic sequence, the first term is 2, and the fourth term is 14. a) Find the common difference, d. b) Calculate the sum of the first 14 terms, S14.

a) We have that a 1 = 2 and a 4 = 14, so the first thing that we can conclude is that the common difference, d, is positive, and that a 2 and a 3 are in between 2 and 14. We know that a 1 + 3d = 14. Substitu...
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Answered by Zhihong Z. • Maths tutor
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