Let y=3^(x). Find (d^(2)y)/(dx^(2)). (d^(2)y)/(dx^(2))=

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Let  y=3^(x). Find  (d^(2)y)/(dx^(2)).  (d^(2)y)/(dx^(2))=

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Find First Derivative: To find the second derivative of y with respect to x, we first need to find the first derivative. The function y = 3^x is an exponential function, and the derivative of an exponential function with base a (where a is a constant) and exponent x is given by the formula dy/dx = a^x * ln(a). In this case, a = 3, so we apply this formula to find the first derivative. Calculation: dy/dx = 3^x * ln(3)Differentiate Again: Now that we have the first derivative, we need to differentiate it once more to find the second derivative. We apply the same rule for differentiation of an exponential function. Calculation: d^2y/dx^2 = d/dx (3^x * ln(3)) = ln(3) * d/dx (3^x) Since ln(3) is a constant, it remains unchanged during differentiation. The derivative of 3^x with respect to x is again 3^x * ln(3).Combine to Find Second Derivative: Combining the constant ln(3) with the derivative of 3^x, we get the second derivative. Calculation: d^2y/dx^2 = ln(3) * (3^x * ln(3)) = (ln(3))^2 * 3^x

Let $y=3^{x}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ . $\newline$ $\frac{d^{2} y}{d x^{2}}=$

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Let $y=3^{x}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ . $\newline$ $\frac{d^{2} y}{d x^{2}}=$