Question

Solve the equation
given by y=x3 in x,dy/DX is
A) 3x² inx
B) 3x² in x + x2
c) x2
D) 3x​

Answer 1

Answer:

B) 3x² ln x + x²

Step-by-step explanation:

Hello!

Differentiation is super fun once you understand how it works!

Your question: x³ Ln x

dy/dx = d(x³ Ln x)/dx

There are two functions, x³ and Ln x

Usually, if u and v are two functions in terms of x,

$\frac{d(uv)}{dx} = u\frac{dv}{dx} + v \frac{du}{dx}$

So, let's apply that here

$\frac{d( {x}^{3} ln \: x)}{dx} = {x}^{3} \frac{d(ln \: x)}{dx} + ln \: x \frac{d( {x}^{3} )}{dx} \\ = ({x}^{3} \times \frac{1}{x} \: ) + (\: ln \: x \times 3 {x}^{2} ) \\ = {x}^{2} + 3 {x}^{2} ln \: x$

Hence, option B

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Hope that helps!

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