A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>Find the derivative of each of the following functions with respect to $x$.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">$f(x) = \log_{7}(5x^{3} + 1)$</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">$f(x) = \frac{\cos x}{\log_{3}(4x^{2} + 1)}$</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">$f(x) = \tan x \log_{2}(5x - 3)$</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">$f(x) = \sin x \log_{6}(3 - 2x)$</div></li></ol>

Find the derivative of each of the following functions with respect to $x$.

$f(x) = \frac{\cos x}{\log_{3}(4x^{2} + 1)}$

Derivatives of Trigonometric Functions

Quotient Rule

Derivatives of Logarithmic Functions (Non-Natural Base)

Product Rule

Chain Rule

Differentiation

<p style="text-align: center">$\frac{\mathrm{d}}{\mathrm{d}x}\left( {{e}^{x}} \right)={{e}^{x}}$</p>
<p style="text-align: center">$\frac{\mathrm{d}}{\mathrm{d}x}\left( {{a}^{x}} \right)={{a}^{x}}\ln a$, where&nbsp;$a&gt;0$ 	</p>
<p style="text-align: center">$\frac{\mathrm{d}}{\mathrm{d}x}\left( \ln x \right)=\frac{1}{x}$</p>
<p style="text-align: center">$\frac{\mathrm{d}}{\mathrm{d}x}\left( {{\log }_{a}}x \right)=\frac{1}{x\ln a}$, where&nbsp;$a&gt;0$</p>

Derivatives of Natural Logarithmic Functions

Derivatives of Exponential Functions

Exponential and Logarithmic Derivatives

Techniques of Differentiation

<p>Find the derivative of each of the following w.r.t $x$:</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = \log_{4}(1 - 3x^{2})$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = \frac{\sin x}{\log_{3}(2x^{2} + 1)}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\mathrm{f}(x) = \sin x \log_{6}(3 - 2x)$</span></div></li></ol>

Find the derivative of each of the following w.r.t $x$:

$y = \frac{\sin x}{\log_{3}(2x^{2} + 1)}$

$\mathrm{f}(x) = \sin x \log_{6}(3 - 2x)$

<p>Find the derivative of each of the following w.r.t $x$:</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$y = \log_{7} (5x^3 + 1)$</div></li><li><div class="list-item-paragraph">$y = \frac{\cos x}{\log_{3} (4x^2 + 1)}$</div></li><li><div class="list-item-paragraph">$\mathrm{f}(x) = \tan x \log_{2} (5x - 3)$</div></li></ol>

\[y = \frac{\cos x}{\log_{3} (4x^2 + 1)}\]

\[\mathrm{f}(x) = \tan x \log_{2} (5x - 3)\]

Further Differentiation

<p>Find the derivatives of the following functions with respect to $x$:</p>
<ol class="i-list"><li><div class="list-item-paragraph">$y = \log_{2}\left( \frac{x}{x-1} \right)$</div></li><li><div class="list-item-paragraph">$y = \log_{5}\left( \frac{x^{2}}{\cos^{3}x} \right)$</div></li><li><div class="list-item-paragraph">$y = \log_{3}\left( \frac{\sqrt{1-x}}{\tan x} \right)$</div></li></ol>

Find the derivatives of the following functions with respect to $x$:

<p>Differentiate the following expressions with respect to $x$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\frac{4{{x}^{3}}+2{{x}^{2}}+1}{x}$</div></li><li><div class="list-item-paragraph">$\mathrm{cose}{{\mathrm{c}}^{3}}\sqrt{x}$</div></li><li><div class="list-item-paragraph">${{\cos }^{2}}\left( x{}^\circ \right)+\tan \left( x{}^\circ \right)$</div></li><li><div class="list-item-paragraph">$\ln \sqrt{\frac{x-a}{x+a}}$ , where $0 < a < x$</div></li><li><div class="list-item-paragraph">$\lg \left( {{x}^{2}} \right)$ , where $x<0$</div></li><li><div class="list-item-paragraph">${{e}^{{{\sin }^{2}}x}}\left( {{e}^{-{{x}^{2}}}}+1 \right)$</div></li></ol>

Differentiate the following expressions with respect to $x$.

Math Question Bank