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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derivative of

(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}

f (x) = \frac{x}{4}

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

n = 2 \sum \infty n^{2} - n

\frac{d}{d z} (\frac{z ^{2}}{2} - \frac{z ^{7}}{7})

\frac{d}{d x} (x cos (x))

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