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{:[y=x^(7)],[(dy)/(dx)=]:}

y=x7dydx= \begin{array}{c}y=x^{7} \\ \frac{d y}{d x}=\end{array}

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Full solution

Q. y=x7dydx= \begin{array}{c}y=x^{7} \\ \frac{d y}{d x}=\end{array}
  1. Given Function: We are given the function y=x7y = x^7 and we need to find its derivative with respect to xx, which is denoted as dydx\frac{dy}{dx} or y′y'. To find the derivative of a power function, we use the power rule, which states that the derivative of xnx^n with respect to xx is n⋅xn−1n \cdot x^{n-1}.
  2. Applying Power Rule: Applying the power rule to our function y=x7y = x^7, we differentiate it as follows:\newlinedydx=7⋅x7−1=7⋅x6\frac{dy}{dx} = 7\cdot x^{7-1} = 7\cdot x^6.
  3. Final Derivative: We have found the derivative of the function y=x7y = x^7 with respect to xx, which is 7x67x^6. There are no calculations to check for errors in this step as it is a direct application of the power rule.

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