Differentiation rules I

Compute the derivatives of each of the following functions using any means that you see fit.

1. f(x) = x^5
2. f(x) = x^{10} - 2x^8 + 4 x^6 - 8x^4 + 16 x^2 - 32
3. f(x) = x^3 + 3^x
4. \displaystyle f(x) = \frac{x^5 - x}{x^3}
5. \displaystyle f(x) = \frac{1}{x^{5/2}}
6. \displaystyle f(x) = \sqrt{x}(x-1)

1.f(x)=x^5
-f'(x)= 5x^4

2.f(x) = x^{10}-2x^8+4x^6-8x^4+16 x^2-32
-f'(x)=10x^9-2(8x^7)+4(6x^5)-8(4x^3)+16(2x)
-f'(x)=10x^9-16x^7+24x^5-24x^3+32x

3.f(x)=x^3+3^x
-f'(x)=3x^2+3^x[ln(3)]

4.f(x)=\frac{x^5 - x}{x^3}
-f'(x)=(x^5-x)(x^{-3})
-f'(x)=x^2-x^{-2}
-f'(x)=2x-(-2x^{-3})
-f'(x)=2x+2x^{-3}

5.f(x)=\frac{1}{x^{5/2}}
-f'(x)=x^{-\frac{5}{2}}
-f'(x)=-\frac{5}{2}x^{-\frac{7}{2}}

6.f(x)=\sqrt{x}(x-1)
-f'(x)=x^{\frac{1}{2}}(x-1)
-f'(x)=-\frac{3}{2}x^{\frac{1}{2}}-\frac{1}{2}x^{-\frac{1}{2}}