A curve has equation y = e^x + 10sin(4x), find the value of the second derivative of this equation at the point x = pi/4.
Firstly, differentiate y with respect to x once to obtain the equation dy/dx = e^x + 40cos(4x). Then differentiate this resultant expression, with respect to x, to acquire a solution for (d^2)y/d(x^2) = e^x - 160sin(4x). The final step of this question is to substitute our value for x (x = pi/4) back into the equation for (d^2)y/d(x^2). This yields the result (d^2)y/d(x^2) = e^(pi/4) at the point x = pi/4.
JI
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