Find the Derivative - d/dx (x^5)/10-16/(x^2)

Problem

d()/d(x)*((x5)/10−16/(x2))

Solution

1. Rewrite the expression using negative exponents to make differentiation easier.

(x5)/10−16*x(−2)

2. Apply the sum rule to differentiate each term independently.

d()/d(x)(x5)/10−d()/d(x)*16*x(−2)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to the first term.

1/10⋅5*x4=1/2*x4

4. Apply the power rule to the second term.

−16⋅(−2)*x(−3)=32*x(−3)

5. Simplify the expression by rewriting the negative exponent as a fraction.

(x4)/2+32/(x3)

Final Answer

d()/d(x)*((x5)/10−16/(x2))=(x4)/2+32/(x3)

Want more problems? Check here!