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Since there is something called a partial derivative in calculus is there a partial integral?
Certainly. It uses the same symbol as the full integral, but you still treat the other independent variables as constants.
What is the derivative of root sin2x?
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
What is the 87th derivative of sin x?
Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
What is the derivative with respect to x of 20xy?
This is technically a partial derivative, represented as ∂(20xy)/∂x. The way to calculate this is simple, treat y as a constant, like 20 is in this case. Therefore, the expression is simplified to 20*y*d(x)/dx. d(x)/dx is just 1, so the answer is 20y.
Prove that a constant vector always has a perpendicular derivative?
A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular
