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Popular >

derivative of (7x^6+2x^3)^4

Solution

derivative of

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

Solution

4 (7 x^{6} + 2 x^{3})^{3} (42 x^{5} + 6 x^{2})

Solution steps

\frac{d}{d x} ((7 x^{6} + 2 x^{3})^{4})

Apply the chain rule:

4 (7 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (7 x^{6} + 2 x^{3})

= 4 (7 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (7 x^{6} + 2 x^{3})

\frac{d}{d x} (7 x^{6} + 2 x^{3}) = 42 x^{5} + 6 x^{2}

= 4 (7 x^{6} + 2 x^{3})^{3} (42 x^{5} + 6 x^{2})

Popular Examples

tangent of sqrt(x+8)tangent of

x + 8

sum from n=0 to infinity of 3^n7^{-n}

n = 0 \sum \infty 3^{n} 7^{- n}

(\partial)/(\partial y)(-xy^2)

\frac{\partial}{\partial y} (- x y^{2})

derivative of y=2xe^{-6x}-4e^{x^3}derivative of

y = 2 x e^{- 6 x} - 4 e^{x^{3}}

tangent of f(x)=(10x)/(x^2-6),(4,4)tangent of

f (x) = \frac{10 x}{x ^{2} - 6}, (4, 4)

Frequently Asked Questions (FAQ)

What is the derivative of (7x^6+2x^3)^4 ?
The derivative of (7x^6+2x^3)^4 is 4(7x^6+2x^3)^3(42x^5+6x^2)
What is the first derivative of (7x^6+2x^3)^4 ?
The first derivative of (7x^6+2x^3)^4 is 4(7x^6+2x^3)^3(42x^5+6x^2)