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.

let y=2 x {take natural logs of both sides} ln y = ln (2 x) {use rules of logs to change right hand side} lny = xln2 {differentiate implicitly} 1/y . dy/dx = ln2 {make dy/dx the subject} dy/ dx = y ln2 …

There are two ways we can find the derivative of x^x. It's important to notice that this function is neither a power function of the form x^k nor an exponential function of the form b^x, so we …

How do I differentiate sin^2 (x)? To differentiate this, we must use the Chain Rule. This is because we have two functions multiplied by each other: (x) sin⁡ (x). We use the substitution u = sin …

Let y = tan (x) Recall the definition of tan (x) as sin (x)/cos (x) Therefore y = sin (x)/cos (x) Use the quotient rule, which states that for y = f (x)/g (x), dy/dx = (f...

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, …

The curve C has the equation: 2 (x^2)y + 2x + 4y – cos (πy) = 17 use implicit differentiation to find dy/dx in terms of x and y

Why is the derivative of x^2 equal to 2x? Differentiation is finding the slope of a graph; how steep it is at some point. In this case, we want to find out how steep the graph of x^2 is.

To differentiate tan (x): Note: Here, we use d/dx f (x) to mean "the derivative of f (x) with respect to x". 1) rewrite tan (x) as sin (x)/cos (x) 2) App...

Mar 20, 2016 · We are being asked to find the normal line at x=1. In order to do that, we take the derivative, evaluate it at at x=1 (which gives us the slope at x=1), then use that information and …