What is the derivative of y=x(x^3+7)^4 ?

The derivative of y=x(x^3+7)^4 is (x^3+7)^4+12x^3(x^3+7)^3

What is the first derivative of y=x(x^3+7)^4 ?

The first derivative of y=x(x^3+7)^4 is (x^3+7)^4+12x^3(x^3+7)^3

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derivative of

y = x (x^{3} + 7)^{4}

(x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{3} + 7)^{4}) = 12 x^{2} (x^{3} + 7)^{3}

= 1 \cdot (x^{3} + 7)^{4} + 12 x^{2} (x^{3} + 7)^{3} x

Simplify

1 \cdot (x^{3} + 7)^{4} + 12 x^{2} (x^{3} + 7)^{3} x : (x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}

= (x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}

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

n = 0 \sum \infty (- \frac{3}{5})^{n}

\int (9 + x^{2})^{- 2} d x

f (x) = x^{3} - 3 x + 1

\int tanh^{2} (x) d x

What is the derivative of y=x(x^3+7)^4 ?
The derivative of y=x(x^3+7)^4 is (x^3+7)^4+12x^3(x^3+7)^3
What is the first derivative of y=x(x^3+7)^4 ?
The first derivative of y=x(x^3+7)^4 is (x^3+7)^4+12x^3(x^3+7)^3