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# Exponentials

/Tag: Exponentials
5 06, 2017

## Challenging Exponentials

Challenging Exponentials Find the derivative of $y=x^x$. let $y = {\left( {{e^{\ln x}}} \right)^x}$ as eln x = x $y = {e^{x.\ln x}}$ let y = eu consider separately u = x.ln x $\frac{du}{dx}=\ln x . 1 + x.\frac{1}{x}$ $\frac{du}{dx}=\ln x +1$ to differentiate y = eu, differentiate [...]

2 08, 2016

10 08, 2015

## Challenging Exponentials & Logs

Challenging Exponentials & Logs Find the equation of the tangent to the curve y = 4x + 1  at the point (0, 4). y = 4x × 41 y = 4.4x y = 4(eln 4)x y = 4ex ln 4 y' = 4ln 4 eln 4 x y' [...]

10 08, 2015

## Integrating e & Log

Integrating e & Log worked examples Find the primitive of:  $\frac{1-xe^x}{x}$. $\frac{1-xe^x}{x}=\frac1x-\frac{xe^x}{x}$ split into two separate fractions to make simplifying a little easier $=\frac1x-e^x$ simplify  y = ln x - ex + c find the primitive (integral), remembering that $\int \frac1x\,dx=ln x+c$ amd $\int e^x dx = e^x+c$ [...]

10 08, 2015

## Tangents and Normals

Tangents & Normals worked examples Find the equation of the normal to the curve y = 3 ln x at the point where x = e.  $y'=\frac3x$ Find y' to find the gradient, as y' = m at x = e y = 3 ln 3 y = [...]

10 08, 2015

## Expon & Log Equations

Expon & Log Equations worked examples Solve 8x = 32x + 1 correct to 3 significant figures. ln 8x = ln 32x + 1 log both sides x ln 8 = (2x + 1) ln 3 using log laws, bring the indices down in front of the ln [...]

10 08, 2015