Derivative by definition, basic differentiation rules

Given  $f\left(x\right)=3x^2+2x-1$  , which of the following is the correct derivative?

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x^2+2x^2-x$  

Given $f\left(x\right)=17$  , what is the derivative of  $f\left(x\right)$  ?

•  $f'\left(x\right)=17x$  

•  $f'\left(x\right)=17$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=17x^2$  

What is the derivative of 0?

• You can't take the derivative of 0.

• 0

• Any function

• Any constant

Differentiate with respect to x.

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Find the derivative for $y=\sqrt{x^5}$  

•  $\frac{5}{2}x^{\frac{7}{2}}$  

•  $\frac{5}{2}x^{\frac{1}{2}}$  

•  $\frac{1}{2}x^{\frac{3}{2}}$  

•  $\frac{5}{2}x^{\frac{3}{2}}$  

Find the derivative for $f\left(x\right)=\left(x+2\right)\left(x^2-3\right)$  

•  $f'\left(x\right)=3x^2-3+4x$  

•  $f'\left(x\right)=3x^2-3x+4x-6$  

•  $f'\left(x\right)=3x^2-3+4x-6$  

•  $f'\left(x\right)=x^3-3x+2x^2-6$  

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line