What is the derivative of y=(x^6-7x+4)(x^4-5x) ?

The derivative of y=(x^6-7x+4)(x^4-5x) is 10x^9-35x^6-35x^4+16x^3+70x-20

What is the first derivative of y=(x^6-7x+4)(x^4-5x) ?

The first derivative of y=(x^6-7x+4)(x^4-5x) is 10x^9-35x^6-35x^4+16x^3+70x-20

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derivative of

y = (x^{6} - 7 x + 4) (x^{4} - 5 x)

10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

Solution steps

\frac{d}{d x} ((x^{6} - 7 x + 4) (x^{4} - 5 x))

Apply the Product Rule:

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

f = x^{6} - 7 x + 4, g = x^{4} - 5 x

= \frac{d}{d x} (x^{6} - 7 x + 4) (x^{4} - 5 x) + \frac{d}{d x} (x^{4} - 5 x) (x^{6} - 7 x + 4)

\frac{d}{d x} (x^{6} - 7 x + 4) = 6 x^{5} - 7

\frac{d}{d x} (x^{4} - 5 x) = 4 x^{3} - 5

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

Simplify

(6 x^{5} - 7) (x^{4} - 5 x) + (4 x^{3} - 5) (x^{6} - 7 x + 4) : 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

= 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

What is the derivative of y=(x^6-7x+4)(x^4-5x) ?
The derivative of y=(x^6-7x+4)(x^4-5x) is 10x^9-35x^6-35x^4+16x^3+70x-20
What is the first derivative of y=(x^6-7x+4)(x^4-5x) ?
The first derivative of y=(x^6-7x+4)(x^4-5x) is 10x^9-35x^6-35x^4+16x^3+70x-20