What is the derivative of 3(5x^4+5x^3^4) ?

The derivative of 3(5x^4+5x^3^4) is 12(5x^4+5x^3)^3(20x^3+15x^2)

What is the first derivative of 3(5x^4+5x^3^4) ?

The first derivative of 3(5x^4+5x^3^4) is 12(5x^4+5x^3)^3(20x^3+15x^2)

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\frac{d}{d x} (3 (5 x^{4} + 5 x^{3})^{4})

12 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

Solution steps

\frac{d}{d x} (3 (5 x^{4} + 5 x^{3})^{4})

Take the constant out:

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

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

Apply the chain rule:

4 (5 x^{4} + 5 x^{3})^{3} \frac{d}{d x} (5 x^{4} + 5 x^{3})

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

\frac{d}{d x} (5 x^{4} + 5 x^{3}) = 20 x^{3} + 15 x^{2}

= 3 \cdot 4 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

Simplify

= 12 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

\int \frac{x ^{2} + 12 x + 12}{x ^{3} - 4 x} d x

\int x^{2} csc^{2} (x) cot (x) d x

\int + sin^{3} (x) cos^{14} (x) d x

\frac{3 x}{x - \frac{3}{x}}

\frac{35}{4 + x + x}

What is the derivative of 3(5x^4+5x^3^4) ?
The derivative of 3(5x^4+5x^3^4) is 12(5x^4+5x^3)^3(20x^3+15x^2)
What is the first derivative of 3(5x^4+5x^3^4) ?
The first derivative of 3(5x^4+5x^3^4) is 12(5x^4+5x^3)^3(20x^3+15x^2)