find the Derivative of::
1\R = 1\R1 + 1\R2
To find the derivative of the expression 1/R = 1/R1 + 1/R2, we can start by rewriting it in a more convenient form:
1/R = R1^(-1) + R2^(-1)
Let's now proceed with taking the derivative.
Step 1: Differentiate both sides with respect to R.
(d/dR) (1/R) = (d/dR) (R1^(-1) + R2^(-1))
Step 2: Apply the power rule for differentiation.
-1/R^2 = -R1^(-2) - R2^(-2)
Step 3: Simplify the expression.
1/R^2 = R1^(-2) + R2^(-2)
Step 4: Rearrange the equation to solve for the derivative.
(d/dR) (1/R) = (1/R^2) = ( R1^(-2) + R2^(-2) )
Therefore, the derivative of the expression 1/R = 1/R1 + 1/R2 is 1/R^2 = R1^(-2) + R2^(-2).
To find the derivative of the expression 1/R = 1/R1 + 1/R2, you can use the quotient rule.
The quotient rule states that if you have a function u(x) divided by v(x), where u(x) and v(x) are both differentiable functions, then the derivative of the quotient is given by:
(d/dx)(u(x)/v(x)) = (v(x)*u'(x) - u(x)*v'(x))/(v(x))^2
To apply the quotient rule to the given expression, let's assign u(x) = 1 and v(x) = R.
Now let's find the derivatives of u(x) and v(x):
u'(x) = 0 (the derivative of a constant is zero)
v'(x) = dR/dx (derivative of R with respect to x)
Now substitute these values into the quotient rule formula:
(d/dx)(1/R) = (R*0 - 1*dR/dx)/(R^2)
= -dR/dx / R^2
Thus, the derivative of 1/R = 1/R1 + 1/R2 with respect to x is -dR/dx / R^2.
This is not a meaningful question absent more information about the symbols.
Are R,R1,R2 functions of x?
Is R a function R(R1,R2)?
This appears to be the solution to a work problem, miscast as a function question.