Find the Derivative - d/dx f(x)=2x^5+6x^8

Problem

d()/d(x)*(2*x5+6*x8)

Solution

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

d()/d(x)*(2*x5+6*x8)=(d(2)*x5)/d(x)+(d(6)*x8)/d(x)

2. Apply the constant multiple rule to move the coefficients outside of the derivatives.

2d(x5)/d(x)+6d(x8)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to each term.

2*(5*x(5−1))+6*(8*x(8−1))

4. Simplify the exponents and multiply the coefficients.

10*x4+48*x7

Final Answer

d()/d(x)*(2*x5+6*x8)=10*x4+48*x7

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