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

The derivative of (2-3x^2^4(x^7+3)^3) is -24x(2-3x^2)^3(x^7+3)^3+21x^6(x^7+3)^2(2-3x^2)^4

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

The first derivative of (2-3x^2^4(x^7+3)^3) is -24x(2-3x^2)^3(x^7+3)^3+21x^6(x^7+3)^2(2-3x^2)^4

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

- 24 x (2 - 3 x^{2})^{3} (x^{7} + 3)^{3} + 21 x^{6} (x^{7} + 3)^{2} (2 - 3 x^{2})^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x^{7} + 3)^{3}) = 21 x^{6} (x^{7} + 3)^{2}

= (- 24 x (2 - 3 x^{2})^{3}) (x^{7} + 3)^{3} + 21 x^{6} (x^{7} + 3)^{2} (2 - 3 x^{2})^{4}

Simplify

= - 24 x (2 - 3 x^{2})^{3} (x^{7} + 3)^{3} + 21 x^{6} (x^{7} + 3)^{2} (2 - 3 x^{2})^{4}

\frac{d y}{d x} + 7 y = 4

\frac{d}{d z} (z + 1 - 1)

x^{2} + 8 x + 2

x \to 1 - lim (\frac{∣ x - 1 ∣}{x - 1})

\frac{d}{d x} (3 - \frac{10}{3 x ^{\frac{1}{6}}})

What is the derivative of (2-3x^2^4(x^7+3)^3) ?
The derivative of (2-3x^2^4(x^7+3)^3) is -24x(2-3x^2)^3(x^7+3)^3+21x^6(x^7+3)^2(2-3x^2)^4
What is the first derivative of (2-3x^2^4(x^7+3)^3) ?
The first derivative of (2-3x^2^4(x^7+3)^3) is -24x(2-3x^2)^3(x^7+3)^3+21x^6(x^7+3)^2(2-3x^2)^4