What is the derivative of f(x)=(5x^3+4)(3x^7-5) ?

The derivative of f(x)=(5x^3+4)(3x^7-5) is 150x^9+84x^6-75x^2

What is the first derivative of f(x)=(5x^3+4)(3x^7-5) ?

The first derivative of f(x)=(5x^3+4)(3x^7-5) is 150x^9+84x^6-75x^2

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derivative of

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

150 x^{9} + 84 x^{6} - 75 x^{2}

Solution steps

\frac{d}{d x} ((5 x^{3} + 4) (3 x^{7} - 5))

Apply the Product Rule:

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

f = 5 x^{3} + 4, g = 3 x^{7} - 5

= \frac{d}{d x} (5 x^{3} + 4) (3 x^{7} - 5) + \frac{d}{d x} (3 x^{7} - 5) (5 x^{3} + 4)

\frac{d}{d x} (5 x^{3} + 4) = 15 x^{2}

\frac{d}{d x} (3 x^{7} - 5) = 21 x^{6}

= 15 x^{2} (3 x^{7} - 5) + 21 x^{6} (5 x^{3} + 4)

Simplify

15 x^{2} (3 x^{7} - 5) + 21 x^{6} (5 x^{3} + 4) : 150 x^{9} + 84 x^{6} - 75 x^{2}

= 150 x^{9} + 84 x^{6} - 75 x^{2}

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What is the derivative of f(x)=(5x^3+4)(3x^7-5) ?
The derivative of f(x)=(5x^3+4)(3x^7-5) is 150x^9+84x^6-75x^2
What is the first derivative of f(x)=(5x^3+4)(3x^7-5) ?
The first derivative of f(x)=(5x^3+4)(3x^7-5) is 150x^9+84x^6-75x^2