What is the derivative of 3x^2(x^3+1^7) ?

The derivative of 3x^2(x^3+1^7) is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)

What is the first derivative of 3x^2(x^3+1^7) ?

The first derivative of 3x^2(x^3+1^7) is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)

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\frac{d}{d x} (3 x^{2} (x^{3} + 1)^{7})

3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

Solution steps

\frac{d}{d x} (3 x^{2} (x^{3} + 1)^{7})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{2} (x^{3} + 1)^{7})

Apply the Product Rule:

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

f = x^{2}, g = (x^{3} + 1)^{7}

= 3 (\frac{d}{d x} (x^{2}) (x^{3} + 1)^{7} + \frac{d}{d x} ((x^{3} + 1)^{7}) x^{2})

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

\frac{d}{d x} ((x^{3} + 1)^{7}) = 21 x^{2} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{2} (x^{3} + 1)^{6} x^{2})

21 x^{2} (x^{3} + 1)^{6} x^{2} = 21 x^{4} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

t^{2} y^{^{''}} - 3 t y^{^{'}} + 4 y = t^{2} \cdot ln (t)

x \to 0 lim (x^{6} ln (x))

\frac{\partial}{\partial x} (\frac{I}{x \cdot y})

5 y^{^{''}} + y^{^{'}} = - 10 x

\frac{4 x}{x + 2}

What is the derivative of 3x^2(x^3+1^7) ?
The derivative of 3x^2(x^3+1^7) is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)
What is the first derivative of 3x^2(x^3+1^7) ?
The first derivative of 3x^2(x^3+1^7) is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)