Given y = x(3x+ 5)^3. Find dy/dx.
First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our functions u and v into this formula, using the chain rule to differentiate v to arrive at dy/dx = (3x + 5)^3 + 9x(3x + 5)^2. Next we need to simplify by taking out a common factor to get (3x + 5)^2 ((3x +5) + 9x)). Which we can further simplify to (3x + 5)^2 (12x + 5) which is the final answer.
MS
Related Maths A Level answers
All answers ▸A stationary point of inflection implies a second derivative of 0, does this work the other way around?
If I am given a line, how do I find a line that is parallel to it? What about perpendicular?
Functions: If f(x)=3x^2 - 4 and g(x) = x + 3, 1) Evaluate f(3), 2) Find the inverse of f(x) (f^-1(x)), 3)Find fg(x).
Given two functions x = at^3 and y = 4a, find dy/dx