What is the derivative of g(x)=4x^2(x^3+5x) ?

The derivative of g(x)=4x^2(x^3+5x) is 4(5x^4+15x^2)

What is the first derivative of g(x)=4x^2(x^3+5x) ?

The first derivative of g(x)=4x^2(x^3+5x) is 4(5x^4+15x^2)

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derivative of

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

4 (5 x^{4} + 15 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = x^{3} + 5 x

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Expand

2 x (x^{3} + 5 x) + (3 x^{2} + 5) x^{2} : 5 x^{4} + 15 x^{2}

= 4 (5 x^{4} + 15 x^{2})

\int (- 8 sec (x) tan (x) + 5 sec^{2} (x)) d x

\frac{d}{d x} ((2 - 7 x^{\frac{3}{2}})^{2})

y^{^{'}} + e^{x} y = 1

2 x^{^{''}} + 4 x^{^{'}} + 8 x = 0, x (0) = 0, x^{^{'}} (0) = 1

\frac{d}{d θ} (e^{- i θ})

What is the derivative of g(x)=4x^2(x^3+5x) ?
The derivative of g(x)=4x^2(x^3+5x) is 4(5x^4+15x^2)
What is the first derivative of g(x)=4x^2(x^3+5x) ?
The first derivative of g(x)=4x^2(x^3+5x) is 4(5x^4+15x^2)