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(d)/(dx)[x^(12)]=

ddx[x12]= \frac{d}{d x}\left[x^{12}\right]=

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Full solution

Q. ddx[x12]= \frac{d}{d x}\left[x^{12}\right]=
  1. Understand Power Rule: We are asked to find the derivative of the function f(x)=x12f(x) = x^{12} with respect to xx. To do this, we will use the power rule for differentiation, which states that if f(x)=xnf(x) = x^n, then f′(x)=n⋅xn−1f'(x) = n \cdot x^{n-1}.
  2. Apply Power Rule: Applying the power rule to our function, we differentiate x12x^{12} with respect to xx. This gives us f′(x)=12⋅x12−1f'(x) = 12\cdot x^{12-1}.
  3. Simplify Exponent: Simplify the exponent in the derivative to get f′(x)=12x11f'(x) = 12x^{11}.
  4. Final Derivative: There are no further simplifications or calculations needed, so we have found the derivative of x12x^{12} with respect to xx.

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