What is the derivative of 10x(x^2+3^4) ?

The derivative of 10x(x^2+3^4) is 10((x^2+3)^4+8x^2(x^2+3)^3)

What is the first derivative of 10x(x^2+3^4) ?

The first derivative of 10x(x^2+3^4) is 10((x^2+3)^4+8x^2(x^2+3)^3)

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\frac{d}{d x} (10 x (x^{2} + 3)^{4})

10 ((x^{2} + 3)^{4} + 8 x^{2} (x^{2} + 3)^{3})

Solution steps

\frac{d}{d x} (10 x (x^{2} + 3)^{4})

Take the constant out:

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

= 10 \frac{d}{d x} (x (x^{2} + 3)^{4})

Apply the Product Rule:

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

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

= 10 (\frac{d x}{d x} (x^{2} + 3)^{4} + \frac{d}{d x} ((x^{2} + 3)^{4}) x)

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

\frac{d}{d x} ((x^{2} + 3)^{4}) = 8 x (x^{2} + 3)^{3}

= 10 (1 \cdot (x^{2} + 3)^{4} + 8 x (x^{2} + 3)^{3} x)

Simplify

10 (1 \cdot (x^{2} + 3)^{4} + 8 x (x^{2} + 3)^{3} x) : 10 ((x^{2} + 3)^{4} + 8 x^{2} (x^{2} + 3)^{3})

= 10 ((x^{2} + 3)^{4} + 8 x^{2} (x^{2} + 3)^{3})

- 46 x sin (x^{2})

y^{^{'}} = e^{5 x + 3 y}

f (t) = cos^{3} (t)

y^{^{''}} - y^{^{'}} - 2 y = e^{3 x} sin (2 x)

y^{^{''}} + y = tan (t) + e^{3 t} - 1

What is the derivative of 10x(x^2+3^4) ?
The derivative of 10x(x^2+3^4) is 10((x^2+3)^4+8x^2(x^2+3)^3)
What is the first derivative of 10x(x^2+3^4) ?
The first derivative of 10x(x^2+3^4) is 10((x^2+3)^4+8x^2(x^2+3)^3)