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Tanny Nusrat
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i have solved the following one but not sure...anyone give me the solve..i want to be sure..
nth derivative of {e^ax * Sin(ax+b)}
nth derivative of {e^ax * Sin(ax+b)}
The formula for finding the nth derivative of e^ax*Sin(ax+b) is:
d^n/dx^n (e^ax*Sin(ax+b)) = a^n*e^ax*Sin(ax+b) + a^(n-1)*cos(ax+b) + a^(n-2)*(-1)^2*sin(ax+b) + ... + a*(-1)^(n-1)*cos(ax+b) + (-1)^n*sin(ax+b)
To solve for the nth derivative of e^ax*Sin(ax+b), you will need to use the formula mentioned in the previous answer. Plug in the value of n and simplify the expression to get the final result.
Yes, you can use the chain rule to find the nth derivative of e^ax*Sin(ax+b). The chain rule states that the derivative of the composition of two functions is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the outer function is e^ax and the inner function is Sin(ax+b).
The values of a and b affect the nth derivative of e^ax*Sin(ax+b) by determining the coefficients of the terms in the final expression. The value of a affects the coefficients of e^ax and cos(ax+b) terms, while the value of b affects the coefficients of Sin(ax+b) and cos(ax+b) terms.
No, there is no shortcut or simpler method to find the nth derivative of e^ax*Sin(ax+b). You will need to use the formula and simplify the expression to get the final result. However, you can use a calculator or computer program to evaluate the expression for a specific value of n, a, and b.