What is the derivative of y=(3+5x)^6(3x^7+2)^3 ?

The derivative of y=(3+5x)^6(3x^7+2)^3 is 30(3+5x)^5(3x^7+2)^3+63x^6(3x^7+2)^2(3+5x)^6

What is the first derivative of y=(3+5x)^6(3x^7+2)^3 ?

The first derivative of y=(3+5x)^6(3x^7+2)^3 is 30(3+5x)^5(3x^7+2)^3+63x^6(3x^7+2)^2(3+5x)^6

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derivative of

y = (3 + 5 x)^{6} (3 x^{7} + 2)^{3}

30 (3 + 5 x)^{5} (3 x^{7} + 2)^{3} + 63 x^{6} (3 x^{7} + 2)^{2} (3 + 5 x)^{6}

Solution steps

\frac{d}{d x} ((3 + 5 x)^{6} (3 x^{7} + 2)^{3})

Apply the Product Rule:

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

f = (3 + 5 x)^{6}, g = (3 x^{7} + 2)^{3}

= \frac{d}{d x} ((3 + 5 x)^{6}) (3 x^{7} + 2)^{3} + \frac{d}{d x} ((3 x^{7} + 2)^{3}) (3 + 5 x)^{6}

\frac{d}{d x} ((3 + 5 x)^{6}) = 30 (3 + 5 x)^{5}

\frac{d}{d x} ((3 x^{7} + 2)^{3}) = 63 x^{6} (3 x^{7} + 2)^{2}

= 30 (3 + 5 x)^{5} (3 x^{7} + 2)^{3} + 63 x^{6} (3 x^{7} + 2)^{2} (3 + 5 x)^{6}

\frac{d}{d x} (7 x sin (π x))

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\int \frac{1}{( x - 1 ) ( x - 2 ) ( x - 3 )} d x

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What is the derivative of y=(3+5x)^6(3x^7+2)^3 ?
The derivative of y=(3+5x)^6(3x^7+2)^3 is 30(3+5x)^5(3x^7+2)^3+63x^6(3x^7+2)^2(3+5x)^6
What is the first derivative of y=(3+5x)^6(3x^7+2)^3 ?
The first derivative of y=(3+5x)^6(3x^7+2)^3 is 30(3+5x)^5(3x^7+2)^3+63x^6(3x^7+2)^2(3+5x)^6