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f(x) = 2/x = 2x^-1
so dy/dx = -2x^-2 = -2/x²
f(x) = 2/x
This can be re-written as f(x) = 2x^-1 according the to the laws of exponents. Now, we just take the derivative normally:
f(x) = 2x^-1
f ' (x) = -1 × 2x^(-1-1) = -2x^-2
The above can be re-written in quotient form as f ' (x) = -2/x²
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What is the derivative of 1 over x?
Derivative of 1/x 1/x = x-1 Take the derivative (-1)x(-1-1) = -x-2 = 1/x2
What is the derivative of 2 to the power of x?
if f(x)=kx, f'(x)=ln(k)*kx. Therefore, the derivative of 2x is ln(2)*2x.
What is the derivative of 1 divided by root x?
(1/2(x^-1/2))/x
How do you find the second derivative?
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
What is the anti derivative of x squared plus x?
The anti-derivative of X2 plus X is the same as the anti-derivative of X2 plus the anti-derivative of X. The anti derivative of X2 is X3/3 plus an integration constant C1 The anti derivative of X is X2/2 plus an integration constant C2 So the anti-derivative of X2+X is (X3/3)+(X2/2)+C1+C2 The constants can be combined and the fraction can combined by using a common denominator leaving (2X3/6)+(3X2/6)+C X2/6 can be factored out leaving (X2/6)(2X+3)+C Hope that helps
What is the derivative of 1 over x?
Derivative of 1/x 1/x = x-1 Take the derivative (-1)x(-1-1) = -x-2 = 1/x2
What is the derivative of 2lnx?
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
What is the derivative of 2x?
-2
What is the derivative of one over x?
1/x = x-1d/dx(x-1) = -x-2 = -1/x2
What is the derivative of e to the power of -2 times x?
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
What is the derivative of e to the power of 2lnx?
Your expression simplifies to just x^2 {with the restriction that x > 0}. The derivative of x^2 is 2*x
What is the anti-derivative of x over 1?
X/1 is just X. so (1/2)X2 + C or X2/2 + C
What is the derivative of square root of x?
sqrt(x) = x^(1/2) The derivative is (1 / 2) * x^(-1 / 2) = 1 / (2 * x^(1 / 2)) = 1 / (2 * sqrt(x))
What is the derivative of x2 plus 6 divided by 2?
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
What is the antiderivative of sqrtx plus 4ex minus sinx?
The anti-derivative of sqrt(x) : sqrt(x)=x^(1/2) The anti-derivative is x^(1/2+1) /(1/2+1) = (2/3) x^(3/2) The anti-derivative is 4e^x is 4 e^x ( I hope you meant e to the power x) The anti-derivative of -sin(x) is cos(x) Adding, the anti-derivative is (2/3) x^(3/2) + 4 e^x + cos(x) + C
What is the derivative of ln x to the power of 2?
If the function is (ln x)2, then the chain rules gives us the derivative 2ln(x)/x, with the x in the denominator. If the function is ln (x2), then the chain rule gives us the derivative 2/x.
What is the derivative of 4 over x?
4/x can be written as 4x-1 (the power of negative 1 means it is the denominator of the fraction) 4*-1 = -4 Therefore, the derivative is -4x-2
