What is the derivative of (5x^7-7x^5+12(3x^6-2x)) ?

The derivative of (5x^7-7x^5+12(3x^6-2x)) is 195x^{12}-231x^{10}-80x^7+300x^5-24

What is the first derivative of (5x^7-7x^5+12(3x^6-2x)) ?

The first derivative of (5x^7-7x^5+12(3x^6-2x)) is 195x^{12}-231x^{10}-80x^7+300x^5-24

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\frac{d}{d x} ((5 x^{7} - 7 x^{5} + 12) (3 x^{6} - 2 x))

195 x^{12} - 231 x^{10} - 80 x^{7} + 300 x^{5} - 24

Solution steps

\frac{d}{d x} ((5 x^{7} - 7 x^{5} + 12) (3 x^{6} - 2 x))

Apply the Product Rule:

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

f = 5 x^{7} - 7 x^{5} + 12, g = 3 x^{6} - 2 x

= \frac{d}{d x} (5 x^{7} - 7 x^{5} + 12) (3 x^{6} - 2 x) + \frac{d}{d x} (3 x^{6} - 2 x) (5 x^{7} - 7 x^{5} + 12)

\frac{d}{d x} (5 x^{7} - 7 x^{5} + 12) = 35 x^{6} - 35 x^{4}

\frac{d}{d x} (3 x^{6} - 2 x) = 18 x^{5} - 2

= (35 x^{6} - 35 x^{4}) (3 x^{6} - 2 x) + (18 x^{5} - 2) (5 x^{7} - 7 x^{5} + 12)

Simplify

(35 x^{6} - 35 x^{4}) (3 x^{6} - 2 x) + (18 x^{5} - 2) (5 x^{7} - 7 x^{5} + 12) : 195 x^{12} - 231 x^{10} - 80 x^{7} + 300 x^{5} - 24

= 195 x^{12} - 231 x^{10} - 80 x^{7} + 300 x^{5} - 24

x \to 1 lim (x + 3)

(x^{3} + 2)^{5}

\frac{\partial}{\partial x} (arctan (x))

\int x^{3} I n x d x

\int \frac{1.05}{1 + 100 e ^{- 0.285 t}} d t

What is the derivative of (5x^7-7x^5+12(3x^6-2x)) ?
The derivative of (5x^7-7x^5+12(3x^6-2x)) is 195x^{12}-231x^{10}-80x^7+300x^5-24
What is the first derivative of (5x^7-7x^5+12(3x^6-2x)) ?
The first derivative of (5x^7-7x^5+12(3x^6-2x)) is 195x^{12}-231x^{10}-80x^7+300x^5-24