26.03 Power rule (ax^n) (Extended)
Differentiate the following:
Differentiate the following, expressing your answers in positive index form.
Differentiate the following:
For each of the following functions:
Differentiate the following functions:
y = \left( 3 x + 2\right) \left( 7 x + 6\right)
y = \left(x + 8\right) \left(x - 7\right) + 5
Find f' \left( 2 \right) if f' \left( x \right) = 4 x^{3} - 3 x^{2} + 4 x - 6.
Consider the graph of f \left( x \right) = - 6 shown:
Find f' \left( 4 \right).
Consider the graph of f \left( x \right) = 2 x - 3:
Find f'\left( - 4 \right).
The tangent to the curve y = 3 + \dfrac{x}{x + 2} at the point \left(0, 3\right) has the equation \\ y = \dfrac{1}{2} x + 3:
Find f' \left( 0 \right).
Consider the graph of the function \\ f \left( x \right) = x^{2}:
How many points on the graph of f \left( x \right) = x^{2} have a gradient of 2?
Find the x-coordinate of the point at which f \left( x \right) = x^{2} has a gradient of 2.
Find the gradient of f \left( x \right) = x^{4} + 7 x at the point \left(2, 30\right):
Consider the function f \left( x \right) = 6 x^{2} + 5 x + 2.
Find f' \left( x \right).
Find f' \left( 2 \right).
Find the x-coordinate of the point at which f' \left( x \right) = 41.
Consider the function f \left( x \right) = x^{3} - 4 x.
Find f' \left( x \right).
Find f' \left( 4 \right).
Find f' \left( - 4 \right).
Find the x-coordinates of the points at which f' \left( x \right) = 71.
Consider the function y = 2 x^{2} - 8 x + 5.
Find \dfrac{dy}{dx}.
Hence, find the value of x at which the gradient is 0.
Find the x-coordinates of the points at which f \left( x \right) = - 3 x^{3} has a gradient of - 81.