That aside, you used the chain rule incorrectly in your solution, which is why it gets the wrong answer.
The differentiation of a constant is 0 as per the constant rule of differentiation. The most direct way to attack the problem is to notice that log(cx)log(c)+log(x) and then obviously, on the right side, we have a constant plus log(x) - and taking the derivative eliminates the constant term. What is The Differentiation of a Constant? We use the differentiation formulas to find the maximum or minimum values of a function, the velocity and acceleration of moving objects, and the tangent of a curve. What Are The Applications of Differentiation Formulas? Constant Rule: y = k f(x), k ≠ 0, then d/dx(k(f(x)) = k d/dx f(x).Chain Rule: Let y = f(u) be a function of u and if u=g(x) so that y = f(g(x), then d/dx(f(g(x))= f'(g(x))g'(x).Quotient Rule: If y = u(x) ÷ v(x), then dy/dx = (v.du/dx- u.dv/dx)/ v 2.Product Rule: If y = u(x) × v(x), then dy/dx = u.dv/dx + v.du/dx.But I cant see how that could be made to happen. And this would be just perfect if the second term was equal to zero. It concerns the derivative of the log of the determinant of a symmetric matrix. Im trying to see why the following theorem is true. Sum Rule: If y = u(x) ± v(x), then dy/dx = du/dx ± dv/dx. Derivative of Log Determinant of a Matrix w.r.t a parameter.The differentiation rules are power rule, chain rule, quotient rule, and the constant rule. There are different rules followed in differentiating a function. We know, slope of the secant line is \(\dfraccos(x+Δx) = cos x\)] What Are The Differentiation Rules?
The slope of a curve at a point is the slope of the tangent line at that point. Take another point Q with coordinates (x+h, f(x+h)) on the curve. Let us take a point P with coordinates(x, f(x)) on a curve. The first principle of differentiation is to compute the derivative of the function using the limits.
The geometrical meaning of the derivative of y = f(x) is the slope of the tangent to the curve y = f(x) at ( x, f(x)).