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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (3 x^{3 x})

\frac{d}{d x} (5 - 2 sin (x) - e^{x})

\int \frac{t}{( 3 t ^{2} + 1 ) ^{4}} d t

y^{^{'}} + y = cos (t), y (0) = 1

y = lo g_{e} (lo g_{e} (x))

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