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# dy/dx & integration

### Extending Differentiation and Integration

What is the derivative of x^n + c? nx^(n-1)
If y = 2x^3 + x^2 + 6, what is dy/dx? 6x^2 + 2x
What is the gradient of y = 2x^3 + x^2 +6 at (4,150)? 104
What is the derivative of (ax + b)^n? (n*a)(ax+b)^(n-1)
Find dy/dx when y = sqrt(3x+2). dy/dx = (3/2)(3x+2)^-1/2
What is the gradient of the curve y = 2(2x+2)^2 + 2 when x = 2? dy/dx = 16x + 16 Gradient = 48
Integrate (ax+b)^n. (((1/a)*(ax+b)^(n+1))/n+1) + c
f(x) = (6x + 4)^2 + 5 What is the integral of f(x)? (6x + 4)^3/18
A curve can be described as y = (x+4)^3 + x^2 What is the gradient when x = 2? dy/dx = 3x^2+26x+48 Gradient = 112
f(x) = cbrt(6x-1) Find f'(x) 2/cbrt((6x-1)^2)
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