Find the Derivative - d/dx y=e^(7x^2)+x

Problem

d()/d(x)*(e(7*x2)+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)*(e(7*x2)+x)=d(e(7*x2))/d(x)+d(x)/d(x)

2. Apply the chain rule to the first term, where the outer function is eu and the inner function is u=7*x2

d(e(7*x2))/d(x)=e(7*x2)⋅(d(7)*x2)/d(x)

3. Differentiate the inner function using the power rule.

(d(7)*x2)/d(x)=14*x

4. Differentiate the second term using the power rule.

d(x)/d(x)=1

5. Combine the results to find the final derivative.

d(y)/d(x)=14*x*e(7*x2)+1

Final Answer

d()/d(x)*(e(7*x2)+x)=14*x*e(7*x2)+1

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