Question

Differentiate e^(4x+5) wrt 10^4x

Answer 1

$</p><p></p><p> \sf \quad \frac{dy}{d( {10}^{4}x) } = \frac{d}{d( {10}^{4}x) } ( {e}^{(4x + 5)} ) \\ \\ \sf \rightarrow \quad \frac{d( {e}^{4x + 5}) }{d(4x + 5)} \cdot \frac{d(4x + 5)}{d( {10}^{4}x) } \\ \\ \sf \rightarrow \quad {e}^{4x + 5} \bigg( \frac{d(4x + 5)}{dx} \cdot \frac{d x }{d( {10}^{4} x)} \bigg) \\ \\ \sf \rightarrow \quad {e}^{4x + 5} \bigg(20x \cdot \frac{1}{ {10}^{4} } \bigg) \\ \\ \sf \rightarrow \quad {e}^{4x + 5} \cdot \frac{x}{500} \\ \\ \sf \rightarrow \quad \frac{x \cdot {e}^{4x + 5} }{500} </p><p>$