# Best Shortcuts of Derivatives

### The Top Ten Best Shortcuts of Derivatives

**d/dx(a*x^b) = (b*a)*(x^(b-1))**

What is this? I don't even

You'll learn about this if you take calculus, it's actually a lot simpler than it looks. - **scienceLover10**

**d/dx(f(g(x))) = f'(g(x)) * g'(x)**

**d/dx(a*b^x) = (ln(b)*a) * (b^x)**

**d/dx(f(x)*g(x)) = f'(x)*g(x) + g'(x)*f(x))**

**d/dx(f(x)+g(x)) = f'(x) + g'(x)**

**d/dx(f(x)/g(x)) = ((f'(x)*g(x)) - (g'(x)*f(x))) / g(x)^2**

**d/dx(a*f(x)) = a * f'(x)**

**d/dx(tan(x)) = sec^2(x)**

**d/dx(sin(x)) = cos(x)**

**d/dx(cos(x)) = -sin(x)**

### The Contenders

**d/dx(ln(x)) = 1/x**

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