What is the derivative of (4x^2+7^2(2x^3+1)^4) ?

The derivative of (4x^2+7^2(2x^3+1)^4) is 16x(4x^2+7)(2x^3+1)^4+24x^2(2x^3+1)^3(4x^2+7)^2

What is the first derivative of (4x^2+7^2(2x^3+1)^4) ?

The first derivative of (4x^2+7^2(2x^3+1)^4) is 16x(4x^2+7)(2x^3+1)^4+24x^2(2x^3+1)^3(4x^2+7)^2

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\frac{d}{d x} ((4 x^{2} + 7)^{2} (2 x^{3} + 1)^{4})

16 x (4 x^{2} + 7) (2 x^{3} + 1)^{4} + 24 x^{2} (2 x^{3} + 1)^{3} (4 x^{2} + 7)^{2}

Solution steps

\frac{d}{d x} ((4 x^{2} + 7)^{2} (2 x^{3} + 1)^{4})

Apply the Product Rule:

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

f = (4 x^{2} + 7)^{2}, g = (2 x^{3} + 1)^{4}

= \frac{d}{d x} ((4 x^{2} + 7)^{2}) (2 x^{3} + 1)^{4} + \frac{d}{d x} ((2 x^{3} + 1)^{4}) (4 x^{2} + 7)^{2}

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

\frac{d}{d x} ((2 x^{3} + 1)^{4}) = 24 x^{2} (2 x^{3} + 1)^{3}

= 16 x (4 x^{2} + 7) (2 x^{3} + 1)^{4} + 24 x^{2} (2 x^{3} + 1)^{3} (4 x^{2} + 7)^{2}

\int \frac{1 + sin ^{2} ( x )}{x} d x

\frac{8 s + 16}{s ^{2} + 8 s + 16}

x \to \infty lim (\frac{cos ( 2 x )}{x ^{2}})

\frac{d}{d x} (3 x - 5 cos^{2} (π x))

4 tan (x^{3} + 2 x^{2})

What is the derivative of (4x^2+7^2(2x^3+1)^4) ?
The derivative of (4x^2+7^2(2x^3+1)^4) is 16x(4x^2+7)(2x^3+1)^4+24x^2(2x^3+1)^3(4x^2+7)^2
What is the first derivative of (4x^2+7^2(2x^3+1)^4) ?
The first derivative of (4x^2+7^2(2x^3+1)^4) is 16x(4x^2+7)(2x^3+1)^4+24x^2(2x^3+1)^3(4x^2+7)^2