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

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

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

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

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\frac{d}{d 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}

2 x^{2} - 3 x, (0, 5)

(3 t - 1)^{4} (2 t + 1)^{- 3}

\int (\frac{x}{1 + x ^{2}}) d x

x \to 4 + lim (\frac{1}{x - 4})

\frac{d y}{d x} = 2 x - y

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