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Popular Calculus >

derivative of 5x^4(3x-7)

Solution

derivative of

5 x^{4} (3 x - 7)

Solution

5 (15 x^{4} - 28 x^{3})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (3 x - 7) = 3

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

Expand

4 x^{3} (3 x - 7) + 3 x^{4} : 15 x^{4} - 28 x^{3}

= 5 (15 x^{4} - 28 x^{3})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 5x^4(3x-7) ?
The derivative of 5x^4(3x-7) is 5(15x^4-28x^3)
What is the first derivative of 5x^4(3x-7) ?
The first derivative of 5x^4(3x-7) is 5(15x^4-28x^3)