Let h(x)=2^(x). Find h^('')(x). h^('')(x)=

Identify Function: Identify the function to differentiate. We are given the function h(x) = 2^x and we need to find its second derivative, denoted as h''(x).Differentiate Once: Differentiate the function once to find the first derivative. The first derivative of h(x) with respect to x is found using the exponential differentiation rule. The derivative of a^x, where a is a constant, is a^x * ln(a). So, h'(x) = d/dx [2^x] = 2^x * ln(2).Differentiate Again: Differentiate the first derivative to find the second derivative. Now we need to differentiate h'(x) = 2^x * ln(2) with respect to x. Using the same rule as before, we get h''(x) = d/dx [2^x * ln(2)] = 2^x * ln(2)^2. However, this is incorrect because the constant ln(2) should not be squared. We need to correct this.

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Let
h(x)=2^(x).
Find
h^('')(x).

h^('')(x)=

Let $h(x)=2^{x}$ . $\newline$ Find $h^{\prime \prime}(x)$ . $\newline$ $h^{\prime \prime}(x)=$

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Algebra 1

Write variable expressions for arithmetic sequences

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Q. Let

h(x)=2^{x}

\newline

Find

h^{\prime \prime}(x)

\newline

h^{\prime \prime}(x)=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $h(x) = 2^x$ and we need to find its second derivative, denoted as $h''(x)$ .
Differentiate Once: Differentiate the function once to find the first derivative. $\newline$ The first derivative of $h(x)$ with respect to $x$ is found using the exponential differentiation rule. The derivative of $a^x$ , where $a$ is a constant, is $a^x \cdot \ln(a)$ . $\newline$ So, $h'(x) = \frac{d}{dx} [2^x] = 2^x \cdot \ln(2)$ .
Differentiate Again: Differentiate the first derivative to find the second derivative. $\newline$ Now we need to differentiate $h'(x) = 2^x \cdot \ln(2)$ with respect to $x$ . $\newline$ Using the same rule as before, we get $h''(x) = \frac{d}{dx} [2^x \cdot \ln(2)] = 2^x \cdot \ln(2)^2$ . $\newline$ However, this is incorrect because the constant $\ln(2)$ should not be squared. We need to correct this.