What is the derivative of (x+5)^6*(x^2+2)^5 ?

The derivative of (x+5)^6*(x^2+2)^5 is 6(x+5)^5(x^2+2)^5+10x(x^2+2)^4(x+5)^6

What is the first derivative of (x+5)^6*(x^2+2)^5 ?

The first derivative of (x+5)^6*(x^2+2)^5 is 6(x+5)^5(x^2+2)^5+10x(x^2+2)^4(x+5)^6

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derivative of

(x + 5)^{6} \cdot (x^{2} + 2)^{5}

6 (x + 5)^{5} (x^{2} + 2)^{5} + 10 x (x^{2} + 2)^{4} (x + 5)^{6}

Solution steps

\frac{d}{d x} ((x + 5)^{6} (x^{2} + 2)^{5})

Apply the Product Rule:

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

f = (x + 5)^{6}, g = (x^{2} + 2)^{5}

= \frac{d}{d x} ((x + 5)^{6}) (x^{2} + 2)^{5} + \frac{d}{d x} ((x^{2} + 2)^{5}) (x + 5)^{6}

\frac{d}{d x} ((x + 5)^{6}) = 6 (x + 5)^{5}

\frac{d}{d x} ((x^{2} + 2)^{5}) = 10 x (x^{2} + 2)^{4}

= 6 (x + 5)^{5} (x^{2} + 2)^{5} + 10 x (x^{2} + 2)^{4} (x + 5)^{6}

What is the derivative of (x+5)^6*(x^2+2)^5 ?
The derivative of (x+5)^6*(x^2+2)^5 is 6(x+5)^5(x^2+2)^5+10x(x^2+2)^4(x+5)^6
What is the first derivative of (x+5)^6*(x^2+2)^5 ?
The first derivative of (x+5)^6*(x^2+2)^5 is 6(x+5)^5(x^2+2)^5+10x(x^2+2)^4(x+5)^6