Find the Derivative - d/dx y=-(x^2)/16+2/x-x^(3/2)+1/(3x^2)+x/3

Problem

d()/d(x)*(−(x2)/16+2/x−x(3/2)+1/(3*x2)+x/3)

Solution

1. Rewrite the expression using negative exponents to prepare for the power rule.

y=−1/16*x2+2*x(−1)−x(3/2)+1/3*x(−2)+1/3*x

2. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term individually.

d(y)/d(x)=−1/16*(2*x)+2*(−1*x(−2))−3/2*x(1/2)+1/3*(−2*x(−3))+1/3*(1)

3. Simplify the coefficients and rewrite the terms with negative exponents as fractions.

d(y)/d(x)=−x/8−2/(x2)−(3√(,x))/2−2/(3*x3)+1/3

Final Answer

d()/d(x)*(−(x2)/16+2/x−x(3/2)+1/(3*x2)+x/3)=−x/8−2/(x2)−(3√(,x))/2−2/(3*x3)+1/3

Want more problems? Check here!