Find the derivative of each of the following w.r.t $x$: $y = \log_{7} (5x^3 + 1)$ \(y = \frac{\c

Question

Find the derivative of each of the following w.r.t $x$: $y = \log_{7} (5x^3 + 1)$ $y = \frac{\cos x}{\log_{3} (4x^2 + 1)}$ $\mathrm{f}(x) = \tan x \log_{2} (5x - 3)$

Accepted Answer

(a) $\frac{15x^2}{(\ln7)(5x^3+1)}$ (b) $-\frac{\ln3[(4x^2+1)\sin x\,\ln(4x^2+1)+8x\cos x]}{(4x^2+1)[\ln(4x^2+1)]^2}$ (c) $\frac{1}{\ln2}[\sec^2x\,\ln(5x-3)+\frac{5\tan x}{5x-3}]$

Further Differentiation

Further Differentiation

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