What is the derivative of y=x^3+4x^2+5x+7 ?

The derivative of y=x^3+4x^2+5x+7 is 3x^2+8x+5

What is the first derivative of y=x^3+4x^2+5x+7 ?

The first derivative of y=x^3+4x^2+5x+7 is 3x^2+8x+5

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derivative of

y = x^{3} + 4 x^{2} + 5 x + 7

3 x^{2} + 8 x + 5

Solution steps

\frac{d}{d x} (x^{3} + 4 x^{2} + 5 x + 7)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (5 x) + \frac{d}{d x} (7)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (5 x) = 5

\frac{d}{d x} (7) = 0

= 3 x^{2} + 8 x + 5 + 0

Simplify

= 3 x^{2} + 8 x + 5

What is the derivative of y=x^3+4x^2+5x+7 ?
The derivative of y=x^3+4x^2+5x+7 is 3x^2+8x+5
What is the first derivative of y=x^3+4x^2+5x+7 ?
The first derivative of y=x^3+4x^2+5x+7 is 3x^2+8x+5