Find the derivative of each of the following functions with respect to $x$. \(f(x) = \log_{7}(5x^{

Question

Find the derivative of each of the following functions with respect to $x$. $f(x) = \log_{7}(5x^{3} + 1)$ $f(x) = \frac{\cos x}{\log_{3}(4x^{2} + 1)}$ $f(x) = \tan x \log_{2}(5x - 3)$ $f(x) = \sin x \log_{6}(3 - 2x)$

Accepted Answer

(i) $\dfrac{15x^2}{(5x^3+1)\ln 7}$ (ii) $\dfrac{\ln3\left[-\sin x\ln(4x^2+1)-\frac{8x\cos x}{4x^2+1}\right]}{[\ln(4x^2+1)]^2}$ (iii) $\sec^2x\log_2(5x-3)+\dfrac{5\tan x}{(5x-3)\ln2}$ (iv) $\cos x\log_6(3-2x)-\dfrac{2\sin x}{(3-2x)\ln6}$

Techniques of Differentiation - Derivatives of Logarithmic Functions (Non-Natural Base)

Techniques of Differentiation - Derivatives of Logarithmic Functions (Non-Natural Base)

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