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

The derivative of 3x^2(2x+5^3) is 3(2x(2x+5)^3+6(2x+5)^2x^2)

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

The first derivative of 3x^2(2x+5^3) is 3(2x(2x+5)^3+6(2x+5)^2x^2)

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

3 (2 x (2 x + 5)^{3} + 6 (2 x + 5)^{2} x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= 3 (2 x (2 x + 5)^{3} + 6 (2 x + 5)^{2} x^{2})

\int \frac{cos ( \frac{π}{x ^{9}} )}{x ^{10}} d x

\int_{1}^{2} t t - 1 d t

x \to c lim (\frac{27}{18})

e^{6 x}

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

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