What is the derivative of 10x(x^2+5)^4 ?

The derivative of 10x(x^2+5)^4 is 10((x^2+5)^4+8x^2(x^2+5)^3)

What is the first derivative of 10x(x^2+5)^4 ?

The first derivative of 10x(x^2+5)^4 is 10((x^2+5)^4+8x^2(x^2+5)^3)

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derivative of

10 x (x^{2} + 5)^{4}

10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

Solution steps

\frac{d}{d x} (10 x (x^{2} + 5)^{4})

Take the constant out:

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

= 10 \frac{d}{d x} (x (x^{2} + 5)^{4})

Apply the Product Rule:

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

f = x, g = (x^{2} + 5)^{4}

= 10 (\frac{d x}{d x} (x^{2} + 5)^{4} + \frac{d}{d x} ((x^{2} + 5)^{4}) x)

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

\frac{d}{d x} ((x^{2} + 5)^{4}) = 8 x (x^{2} + 5)^{3}

= 10 (1 \cdot (x^{2} + 5)^{4} + 8 x (x^{2} + 5)^{3} x)

Simplify

10 (1 \cdot (x^{2} + 5)^{4} + 8 x (x^{2} + 5)^{3} x) : 10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

= 10 ((x^{2} + 5)^{4} + 8 x^{2} (x^{2} + 5)^{3})

y = 2 e^{3} t

\int (4 x (3 x - 2)) d x

\frac{d}{d x} (2 a arccos (2 x))

sin^{4} (6 x^{2})

\int 11 x^{\frac{4}{7}} + 8 x^{- \frac{6}{7}} d x

What is the derivative of 10x(x^2+5)^4 ?
The derivative of 10x(x^2+5)^4 is 10((x^2+5)^4+8x^2(x^2+5)^3)
What is the first derivative of 10x(x^2+5)^4 ?
The first derivative of 10x(x^2+5)^4 is 10((x^2+5)^4+8x^2(x^2+5)^3)