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# dy/dx & integration

### Extending Differentiation and Integration

Question | Answer |
---|---|

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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