What is the derivative of x^3(x^2+1)^7 ?

The derivative of x^3(x^2+1)^7 is 3x^2(x^2+1)^7+14x^4(x^2+1)^6

What is the first derivative of x^3(x^2+1)^7 ?

The first derivative of x^3(x^2+1)^7 is 3x^2(x^2+1)^7+14x^4(x^2+1)^6

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derivative of

x^{3} (x^{2} + 1)^{7}

3 x^{2} (x^{2} + 1)^{7} + 14 x^{4} (x^{2} + 1)^{6}

Solution steps

\frac{d}{d x} (x^{3} (x^{2} + 1)^{7})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = (x^{2} + 1)^{7}

= \frac{d}{d x} (x^{3}) (x^{2} + 1)^{7} + \frac{d}{d x} ((x^{2} + 1)^{7}) x^{3}

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

\frac{d}{d x} ((x^{2} + 1)^{7}) = 14 x (x^{2} + 1)^{6}

= 3 x^{2} (x^{2} + 1)^{7} + 14 x (x^{2} + 1)^{6} x^{3}

14 x (x^{2} + 1)^{6} x^{3} = 14 x^{4} (x^{2} + 1)^{6}

= 3 x^{2} (x^{2} + 1)^{7} + 14 x^{4} (x^{2} + 1)^{6}

What is the derivative of x^3(x^2+1)^7 ?
The derivative of x^3(x^2+1)^7 is 3x^2(x^2+1)^7+14x^4(x^2+1)^6
What is the first derivative of x^3(x^2+1)^7 ?
The first derivative of x^3(x^2+1)^7 is 3x^2(x^2+1)^7+14x^4(x^2+1)^6