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

Problem

d()/d(x)*(5*x2+cos(x))

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)*(5*x2+cos(x))=(d(5)*x2)/d(x)+d(cos(x))/d(x)

2. Apply the power rule to the first term, where the derivative of a*xn is a*n*x(n−1)

(d(5)*x2)/d(x)=10*x

3. Apply the trigonometric rule to the second term, where the derivative of cos(x) is −sin(x)

d(cos(x))/d(x)=−sin(x)

4. Combine the results to find the final derivative of the expression.

d(y)/d(x)=10*x−sin(x)

Final Answer

d()/d(x)*(5*x2+cos(x))=10*x−sin(x)

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