What is the derivative of $e^{x^{3}} + {log}_{5} (π)$ $e^(x^3)+log_5(pi)$ ?

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What is the derivative of $e^{x^{3}} + {log}_{5} (π)$ $e^(x^3)+log_5(pi)$ ?

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Answer 1 · 2018-03-03T09:36:44

$\frac{d}{d x} e^{x^{3}} + {log}_{5} (π) = 3 x^{2} e^{x^{3}}$ $d/dx e^(x^3) + log_5(pi) = 3x^2e^(x^3)$

Explanation:

The ${log}_{5} (π)$ $log_5 (pi)$ is a constant, so the derivative of the function can be turned down to a simpler $\frac{d}{d x} e^{x^{3}}$ $d/dx e^(x^3)$ .

Let $y$ $y$ be equal to $e^{x^{3}}$ $e^(x^3)$ . Take the natural logarithm of both sides.

$ln y = x^{3} \cdot ln e$ $ln y = x^3 *ln e$
$ln y = x^{3}$ $ln y= x^3$

Differentiate both :

$\frac{d y}{d x} \frac{1}{y} = 3 x^{2}$ $dy/dx 1/y = 3x^2$

$\frac{d y}{d x} = y \cdot 3 x^{2} = 3 x^{2} e^{x^{3}}$ $dy/dx = y*3x^2 = 3x^2e^(x^3)$ , so

$\frac{d}{d x} e^{x^{3}} + {log}_{5} (π) = 3 x^{2} e^{x^{3}}$ $color(blue)(d/dx e^(x^3) + log_5(pi) = 3x^2e^(x^3))$ .

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What is the derivative of $e^{x^{3}} + {log}_{5} (π)$ $e^(x^3)+log_5(pi)$ ?

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