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Popular >

derivative of (8(4x^4+5)^3)

Solution

\frac{d}{d x} ((8 (4 x)^{4} + 5)^{3})

Solution

24576 x^{3} (2048 x^{4} + 5)^{2}

Solution steps

\frac{d}{d x} ((8 (4 x)^{4} + 5)^{3})

Simplify

(8 (4 x)^{4} + 5)^{3} : (2048 x^{4} + 5)^{3}

= \frac{d}{d x} ((2048 x^{4} + 5)^{3})

Apply the chain rule:

3 (2048 x^{4} + 5)^{2} \frac{d}{d x} (2048 x^{4} + 5)

= 3 (2048 x^{4} + 5)^{2} \frac{d}{d x} (2048 x^{4} + 5)

\frac{d}{d x} (2048 x^{4} + 5) = 8192 x^{3}

= 3 (2048 x^{4} + 5)^{2} \cdot 8192 x^{3}

Simplify

= 24576 x^{3} (2048 x^{4} + 5)^{2}

Popular Examples

(\partial)/(\partial y)(arctan(x)y)

\frac{\partial}{\partial y} (arctan (x) y)

tangent of 4-ln(x)tangent of

4 - ln (x)

y^{''}+4y^'+40y=40cos(8t)

y^{^{''}} + 4 y^{^{'}} + 40 y = 40 cos (8 t)

(\partial)/(\partial x)(1/(3x))

\frac{\partial}{\partial x} (\frac{1}{3 x})

integral of 1+4x

\int 1 + 4 x d x

Frequently Asked Questions (FAQ)

What is the derivative of (8(4x^4+5)^3) ?
The derivative of (8(4x^4+5)^3) is 24576x^3(2048x^4+5)^2
What is the first derivative of (8(4x^4+5)^3) ?
The first derivative of (8(4x^4+5)^3) is 24576x^3(2048x^4+5)^2