Find the Derivative - d/dx e^(7x^2+3)

Problem

d(e(7*x2+3))/d(x)

Solution

1. Identify the outer function as the exponential function eu and the inner function as u=7*x2+3

2. Apply the chain rule, which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the inner function 7*x2+3 with respect to x using the power rule.

d(7*x2+3)/d(x)=14*x

4. Multiply the derivative of the outer function by the derivative of the inner function.

d(e(7*x2+3))/d(x)=e(7*x2+3)⋅14*x

5. Rearrange the terms to write the derivative in standard form.

d(e(7*x2+3))/d(x)=14*x*e(7*x2+3)

Final Answer

d(e(7*x2+3))/d(x)=14*x*e(7*x2+3)

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