What is the derivative of 20x(2x^2+7)^4 ?

The derivative of 20x(2x^2+7)^4 is 20((2x^2+7)^4+16x^2(2x^2+7)^3)

What is the first derivative of 20x(2x^2+7)^4 ?

The first derivative of 20x(2x^2+7)^4 is 20((2x^2+7)^4+16x^2(2x^2+7)^3)

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derivative of

20 x (2 x^{2} + 7)^{4}

20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

Solution steps

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})

Take the constant out:

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

= 20 \frac{d}{d x} (x (2 x^{2} + 7)^{4})

Apply the Product Rule:

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

f = x, g = (2 x^{2} + 7)^{4}

= 20 (\frac{d x}{d x} (2 x^{2} + 7)^{4} + \frac{d}{d x} ((2 x^{2} + 7)^{4}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x^{2} + 7)^{4}) = 16 x (2 x^{2} + 7)^{3}

= 20 (1 \cdot (2 x^{2} + 7)^{4} + 16 x (2 x^{2} + 7)^{3} x)

Simplify

20 (1 \cdot (2 x^{2} + 7)^{4} + 16 x (2 x^{2} + 7)^{3} x) : 20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

= 20 ((2 x^{2} + 7)^{4} + 16 x^{2} (2 x^{2} + 7)^{3})

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

\int_{0}^{π} 5 sin^{2} (2 x) d x

f (x) = (x - 5) (2 x + 5)

\int 8 (x + 1) \cdot ln (x + 1) d x

f (x) = \frac{10 x - 4}{3 x + 8}

What is the derivative of 20x(2x^2+7)^4 ?
The derivative of 20x(2x^2+7)^4 is 20((2x^2+7)^4+16x^2(2x^2+7)^3)
What is the first derivative of 20x(2x^2+7)^4 ?
The first derivative of 20x(2x^2+7)^4 is 20((2x^2+7)^4+16x^2(2x^2+7)^3)