Turunan dari $$$\frac{\ln\left(a\right)}{\ln\left(b\right)}$$$ terhadap $$$a$$$
Kalkulator terkait: Kalkulator Diferensiasi Logaritmik, Kalkulator Diferensiasi Implisit dengan Langkah-langkah
Masukan Anda
Temukan $$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)$$$.
Solusi
Terapkan aturan kelipatan konstanta $$$\frac{d}{da} \left(c f{\left(a \right)}\right) = c \frac{d}{da} \left(f{\left(a \right)}\right)$$$ dengan $$$c = \frac{1}{\ln\left(b\right)}$$$ dan $$$f{\left(a \right)} = \ln\left(a\right)$$$:
$${\color{red}\left(\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{da} \left(\ln\left(a\right)\right)}{\ln\left(b\right)}\right)}$$Turunan dari logaritma natural adalah $$$\frac{d}{da} \left(\ln\left(a\right)\right) = \frac{1}{a}$$$:
$$\frac{{\color{red}\left(\frac{d}{da} \left(\ln\left(a\right)\right)\right)}}{\ln\left(b\right)} = \frac{{\color{red}\left(\frac{1}{a}\right)}}{\ln\left(b\right)}$$Dengan demikian, $$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right) = \frac{1}{a \ln\left(b\right)}$$$.
Jawaban
$$$\frac{d}{da} \left(\frac{\ln\left(a\right)}{\ln\left(b\right)}\right) = \frac{1}{a \ln\left(b\right)}$$$A