What is the derivative of [3(3x^5+6)^3](12x^3) ?

The derivative of [3(3x^5+6)^3](12x^3) is 36(3x^2(3x^5+6)^3+45x^7(3x^5+6)^2)

What is the first derivative of [3(3x^5+6)^3](12x^3) ?

The first derivative of [3(3x^5+6)^3](12x^3) is 36(3x^2(3x^5+6)^3+45x^7(3x^5+6)^2)

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derivative of

[3 (3 x^{5} + 6)^{3}] (12 x^{3})

36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})

Solution steps

\frac{d}{d x} ((3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3})

Simplify

(3 (3 x^{5} + 6)^{3}) \cdot 12 x^{3} : 36 x^{3} (3 x^{5} + 6)^{3}

= \frac{d}{d x} (36 x^{3} (3 x^{5} + 6)^{3})

Take the constant out:

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

= 36 \frac{d}{d x} (x^{3} (3 x^{5} + 6)^{3})

Apply the Product Rule:

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

f = x^{3}, g = (3 x^{5} + 6)^{3}

= 36 (\frac{d}{d x} (x^{3}) (3 x^{5} + 6)^{3} + \frac{d}{d x} ((3 x^{5} + 6)^{3}) x^{3})

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

\frac{d}{d x} ((3 x^{5} + 6)^{3}) = 45 x^{4} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{4} (3 x^{5} + 6)^{2} x^{3})

45 x^{4} (3 x^{5} + 6)^{2} x^{3} = 45 x^{7} (3 x^{5} + 6)^{2}

= 36 (3 x^{2} (3 x^{5} + 6)^{3} + 45 x^{7} (3 x^{5} + 6)^{2})

x = 9 y^{3}, x = 23 y^{2}

\frac{\partial}{\partial z} (e^{x y})

f (x) = (2 x + 1)^{5}

\frac{( 1 - x )}{( x + 2 )}

x^{3} y^{^{'}} + 4 x^{2} y = e^{- x}

What is the derivative of [3(3x^5+6)^3](12x^3) ?
The derivative of [3(3x^5+6)^3](12x^3) is 36(3x^2(3x^5+6)^3+45x^7(3x^5+6)^2)
What is the first derivative of [3(3x^5+6)^3](12x^3) ?
The first derivative of [3(3x^5+6)^3](12x^3) is 36(3x^2(3x^5+6)^3+45x^7(3x^5+6)^2)