What is the derivative of the area of a circle?

circumferenceequals its circumference—is extended to other shapes and solids.

What’s the derivative of the area of a circle?

. That is, the derivative of the area is just the circumference.

How do you find the derivative of an area?

The derivative of the area function A(x) is f(x), so A(x) is an antiderivative of f(x). As both A(x) and F(x) are antiderivatives of f(x), they must differ by a constant, i.e., A(x)=F(x)+K for some constant K.

What does the derivative of an area represent?

The derivative measures the rate at which the area changes when the side changes, measured in units like (square centimeters of area) per (centimeter of side).

What is the derivative of r 2?

Since r2 is constant with respect to h , the derivative of r2 with respect to h is 0 .

Why is the derivative of pi r 2?

When differentiated with respect to r, the derivative of πr2 is 2πr, which is the circumference of a circle. Similarly, when the formula for a sphere’s volume 43πr3 is differentiated with respect to r, we get 4πr2.

What is the derivative of pi 3?

0

Since π3 is constant with respect to x , the derivative of π3 with respect to x is 0 .

What is the derivative of 4/3 pi r3?

Since 4π3 4 π 3 is constant with respect to r , the derivative of 4πr33 4 π r 3 3 with respect to r is 4π3ddr[r3] 4 π 3 d d r [ r 3 ] .

What is the derivative of pi 4?

1 Answer. Daniel L. The derivative of π4 is 0 .

What is the derivative of 2x?

2

The derivative of 2x is equal to 2 as the formula for the derivative of a straight line function f(x) = ax + b is given by f'(x) = a, where a, b are real numbers. Differentiation of 2x is calculated using the formula d(ax+b)/dx = a.

What is the derivative of sinx?

cos x

The derivative of sin x is denoted by d/dx (sin x) = cos x. The other way to represent the sine function is (sin x)’ = cos x.

What is the derivative of Pi 2?

0

Since π2 is constant with respect to x , the derivative of π2 with respect to x is 0 .

What is the derivative of 1?

zero

Derivative of 1 is zero. Reason: Derivative of a constant term is always zero.

Is the derivative of pi 0?

π is just a constant, meaning it doesn’t change with respect to a variable . It will graph as a horizontal line, just like 2,8, and 11 will. As we know, slopes of horizontal lines are 0 , so the derivative of a constant, like π , will always be zero.

What is the derivative of TANX?

sec²x

We know that the derivative of tan x is sec²x. Also, sec x = 1/(cos x).

What is the derivative of sin2x?

2 cos 2x

The derivative of sin 2x is 2 cos 2x.

What is derivative of Arcsin?

What is Derivative of arcsin? The derivative of arcsin x is 1/√1-x². It is written as d/dx(arcsin x) = 1/√1-x². This also can be written as d/dx(sin^–1x) = 1/√1-x².

What is the derivative of LNX?

1/x

The derivative of ln(x) is 1/x.

What does Lnx equal?

log_e(x)

The natural log simply lets people reading the problem know that you’re taking the logarithm, with a base of e, of a number. So ln(x) = log_e(x).

What does LNE equal to?

1

The natural logarithm of e itself, ln e, is 1, because e¹ = e, while the natural logarithm of 1 is 0, since e⁰ = 1.

What is the derivative of ln y?

1/

The derivative of ln y is 1/ (derivative of f = e^x) = 1/e^x.