Find the Derivative - d/dx f(x)=-1/2+7/5x^3

Problem

d()/d(x)*(−1/2+7/5*x3)

Solution

1. Identify the function as a sum of two terms: a constant term −1/2 and a power term 7/5*x3

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

3. Differentiate the constant term −1/2 The derivative of any constant with respect to x is 0

d()/d(x)−1/2=0

4. Apply the power rule to the term 7/5*x3 Multiply the coefficient by the exponent and decrease the exponent by 1

d()/d(x)7/5*x3=7/5⋅3*x(3−1)

5. Simplify the resulting expression by performing the multiplication.

21/5*x2

Final Answer

d()/d(x)*(−1/2+7/5*x3)=21/5*x2

Want more problems? Check here!