What is the derivative of 4 Pi R Square?

Since 4π is constant with respect to r , the derivative of 4πr2 4 π r 2 with respect to r is 4πddr[r2] 4 π d d r [ r 2 ] .

What is the derivative of pi r 2 H?

Calculus Examples Since πh π h is constant with respect to r r , the derivative of πr2h π r 2 h with respect to r r is πhddr[r2] π h d d r [ r 2 ] .

What is the derivative of PIR?

When differentiated with respect to r, the derivative of πr2 is 2πr, which is the circumference of a circle.

What is V pi * r 2 * H?

The formula for the volume of a cylinder is V=π r(squared) h Solve V=π r(squared) h for h, the height of the cylinder.

What is 4/3 pi r cubed?

The formula for the volume of a sphere is V = 4/3 πr³.

What is the derivative of PI 3?

Since π3 is constant with respect to , the derivative of π3 with respect to 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 formula is pi r squared h?

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm.

Why is the volume of a sphere 4 3 pi r squared?

Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3.

Why is surface area of a sphere 4 pi r squared?

One geometric explanation is that 4πr2 is the derivative of 43πr3, the volume of the ball with radius r, with respect to r. This is because if you enlarge r a little bit, the volume of the ball will change by its surface times the small enlargement of r.

How to calculate the derivative of f ( x ) x?

Given a function f (x) f ( x), there are many ways to denote the derivative of f f with respect to x x. The most common ways are df dx d f d x and f ′(x) f ′ ( x).

What do you call a second order derivative?

These are called higher-order derivatives. Note for second-order derivatives, the notation f ′′(x) f ″ ( x) is often used. At a point x = a x = a, the derivative is defined to be f ′(a) = lim h→0 f(a+h)−f(h) h f ′ ( a) = lim h → 0 f ( a + h) − f ( h) h.

How to calculate a derivative in Wolfram Alpha?

How Wolfram|Alpha calculates derivatives. Wolfram|Alpha calls Wolfram Languages’s D function, which uses a table of identities much larger than one would find in a standard calculus textbook. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. Additionally, D uses lesser-known rules

Which is the best derivative calculator to use?

Wolfram|Alpha is a great calculator for first, second and third derivatives; derivatives at a point; and partial derivatives. Learn what derivatives are and how Wolfram|Alpha calculates them. Enter your queries using plain English.