Photo AI

Given that $y = rac{3}{5} \cdot \frac{10}{x^2}$, where $x \neq 0$, find \( \frac{dy}{dx} \). - Scottish Highers Maths - Question 1 - 2023

Question icon

Question 1

Given-that-$y-=--rac{3}{5}-\cdot-\frac{10}{x^2}$,-where-$x-\neq-0$,-find-\(-\frac{dy}{dx}-\).-Scottish Highers Maths-Question 1-2023.png

Given that $y = rac{3}{5} \cdot \frac{10}{x^2}$, where $x \neq 0$, find \( \frac{dy}{dx} \).

Worked Solution & Example Answer:Given that $y = rac{3}{5} \cdot \frac{10}{x^2}$, where $x \neq 0$, find \( \frac{dy}{dx} \). - Scottish Highers Maths - Question 1 - 2023

Step 1

Express second term in differentiable form

96%

114 rated

Answer

First, rewrite the function in a clearer form. We have:

y=305⋅x−2=6x−2y = \frac{30}{5} \cdot x^{-2} = 6x^{-2}

Step 2

Differentiate one term

99%

104 rated

Answer

Next, differentiate the term using the power rule:

dydx=6⋅(−2)x−3=−12x−3\frac{dy}{dx} = 6 \cdot (-2)x^{-3} = -12x^{-3}

Step 3

Complete differentiation

96%

101 rated

Answer

Thus, the complete differentiation gives the final result:

dydx=−12x3\frac{dy}{dx} = -\frac{12}{x^3}

Join the Scottish Highers students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;