What is the derivative of x^5(3+8x)^7 ?

The derivative of x^5(3+8x)^7 is 5x^4(3+8x)^7+56(3+8x)^6x^5

What is the first derivative of x^5(3+8x)^7 ?

The first derivative of x^5(3+8x)^7 is 5x^4(3+8x)^7+56(3+8x)^6x^5

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derivative of

x^{5} (3 + 8 x)^{7}

5 x^{4} (3 + 8 x)^{7} + 56 (3 + 8 x)^{6} x^{5}

Solution steps

\frac{d}{d x} (x^{5} (3 + 8 x)^{7})

Apply the Product Rule:

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

f = x^{5}, g = (3 + 8 x)^{7}

= \frac{d}{d x} (x^{5}) (3 + 8 x)^{7} + \frac{d}{d x} ((3 + 8 x)^{7}) x^{5}

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

\frac{d}{d x} ((3 + 8 x)^{7}) = 56 (3 + 8 x)^{6}

= 5 x^{4} (3 + 8 x)^{7} + 56 (3 + 8 x)^{6} x^{5}

What is the derivative of x^5(3+8x)^7 ?
The derivative of x^5(3+8x)^7 is 5x^4(3+8x)^7+56(3+8x)^6x^5
What is the first derivative of x^5(3+8x)^7 ?
The first derivative of x^5(3+8x)^7 is 5x^4(3+8x)^7+56(3+8x)^6x^5