Find the Derivative - d/dx y=5/((2x)^3)+2cos(x)

Problem

d()/d(x)*(5/((2*x)3)+2*cos(x))

Solution

1. Simplify the first term by applying the power to the denominator.

5/((2*x)3)=5/(8*x3)

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

y=5/8*x(−3)+2*cos(x)

3. Apply the power rule to the first term by multiplying the coefficient by the exponent and subtracting one from the exponent.

d()/d(x)5/8*x(−3)=5/8⋅(−3)*x(−4)

4. Apply the derivative rule for the trigonometric term, where d(cos(x))/d(x)=−sin(x)

d()/d(x)*2*cos(x)=−2*sin(x)

5. Simplify the resulting expression and rewrite the negative exponent as a fraction.

d(y)/d(x)=−15/(8*x4)−2*sin(x)

Final Answer

d()/d(x)*(5/((2*x)3)+2*cos(x))=−15/(8*x4)−2*sin(x)

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