How do you differentiate y2 with respect to X?

Notice what we have just done. In order to differentiate y2 with respect to x we have differentiated y2 with respect to y, and then multiplied by dy dx , i.e. This is our expression for dy dx . As before, we differentiate each term with respect to x.

What is the differentiation of x 2y?

If this is single variable calculus, then we do logarithmic differentiation. So, say z=x^(2y) then ln z=2y*ln x now differentiate. Then 1/z dz/dx=2 dy/dx ln x + 2y/x. the derivative then becomes z*(2dy/dx ln x + 2y/x)=x^(2y)*(2 dy/dx ln x + 2y/x).

What is the derivative with respect to x of x?

The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called the derivative of f with respect to x.

How do you differentiate with respect to X?

Differentiate with respect to x: d dx (x 2) + d dx (y 2) = d dx (r 2) Let’s solve each term: Use the Power Rule: d dx (x2) = 2x

How do you differentiate X 2 + y 2 = 3x?

However, there are cases when the only possible method is (3). Differentiate x 2 + y 2 = 3x, with respect to x. Differentiate a x with respect to x. You might be tempted to write xa x-1 as the answer. This is wrong. That would be the answer if we were differentiating with respect to a not x. Put y = a x .

How do you find the derivative of X with respect to R2?

Differentiate with respect to x: d dx (x 2) + d dx (y 2) = d dx (r 2) Let’s solve each term: Use the Power Rule: d dx (x2) = 2x. Use the Chain Rule (explained below): d dx (y2) = 2y dy dx. r 2 is a constant, so its derivative is 0: d dx (r2) = 0. Which gives us: 2x + 2y dy dx = 0. Collect all the dy dx on one side.

What is dy dx = 1 2y?

Derivative: 2y dy dx = 1 Simplify: dy dx = 1 2y Because y = √x: dy dx = 1 2√x Note: this is the same answer we get using the Power Rule: