able 16^(x^2)+y+16^x+y^2

Identify terms and apply derivatives: Identify the terms involving x and apply the derivative rules separately to each term. - Derivative of 16^(x^2) with respect to x: Using the chain rule, d/dx[16^(x^2)] = 16^(x^2) * ln(16) * 2x. - Derivative of y with respect to x: Since y is treated as a constant with respect to x, dy/dx = 0. - Derivative of 16^x with respect to x: Using the exponential rule, d/dx[16^x] = 16^x * ln(16). - Derivative of y^2 with respect to x: Since y^2 is treated as a constant with respect to x, d/dx[y^2] = 0.Combine derivatives for entire function: Combine the derivatives to form the derivative of the entire function. - f'(x) = 16^(x^2) * ln(16) * 2x + 0 + 16^x * ln(16) + 0. - Simplify the expression: f'(x) = 16^(x^2) * 2x * ln(16) + 16^x * ln(16).

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Find derivatives using the product rule II

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16^{x^2}+y+16^x+y^2

Identify terms and apply derivatives: Identify the terms involving $x$ and apply the derivative rules separately to each term. $\newline$ - Derivative of $16^{x^2}$ with respect to $x$ : Using the chain rule, $\frac{d}{dx}[16^{x^2}] = 16^{x^2} \cdot \ln(16) \cdot 2x$ . $\newline$ - Derivative of $y$ with respect to $x$ : Since $y$ is treated as a constant with respect to $x$ , $\frac{dy}{dx} = 0$ . $\newline$ - Derivative of $16^x$ with respect to $x$ : Using the exponential rule, $16^{x^2}$ $1$ . $\newline$ - Derivative of $16^{x^2}$ $2$ with respect to $x$ : Since $16^{x^2}$ $2$ is treated as a constant with respect to $x$ , $16^{x^2}$ $6$ .
Combine derivatives for entire function: Combine the derivatives to form the derivative of the entire function. $\newline$ - $f'(x) = 16^{x^2} \cdot \ln(16) \cdot 2x + 0 + 16^x \cdot \ln(16) + 0$ . $\newline$ - Simplify the expression: $f'(x) = 16^{x^2} \cdot 2x \cdot \ln(16) + 16^x \cdot \ln(16)$ .