differentiate the function R(x)=sqrt(10)/x^7
y = 10^.5 * x^-7
dy/dx = (-7) * (10^.5) * x^-8
To differentiate the function R(x) = sqrt(10)/x^7, we can use the power rule for differentiation and the chain rule.
The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1).
In this case, we have a constant (sqrt(10)) multiplied by x^(-7). Applying the power rule, we differentiate each part separately.
1. Differentiating sqrt(10):
The derivative of sqrt(10) is 0 because it is a constant.
2. Differentiating x^(-7):
Using the power rule, we get (-7)(x^(-7-1)) = -7x^(-8) = -7/x^8.
Combining the derivatives of the two parts, we get:
R'(x) = (0)(x^(-7)) - (sqrt(10))(7/x^8) = -7sqrt(10)/x^8.
Therefore, the derivative of R(x) = sqrt(10)/x^7 is R'(x) = -7sqrt(10)/x^8.