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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 cr...

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...

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 = -16x² + 160x - 256

x = 5

y = 144

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 coordi...

Answered by Georgios Marios P. • Maths tutor

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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 a₁ = 2 and a₄ = 14, so the first thing that we can conclude is that the common difference, d, is positive, and that a₂ and a₃ are in between 2 a...

Answered by Zhihong Z. • Maths tutor

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