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Popular >

derivative of f(x)=(x^5-x^3+3)^4

Solution

derivative of

f (x) = (x^{5} - x^{3} + 3)^{4}

Solution

4 (x^{5} - x^{3} + 3)^{3} (5 x^{4} - 3 x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Popular Examples

(d^2y)/(dx^2)-7(dy)/(dx)+12y=0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 12 y = 0

integral of ((x^3-5x+2))/(x^{1/2)}

\int \frac{( x ^{3} - 5 x + 2 )}{x ^{\frac{1}{2}}} d x

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

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

integral of x^3sqrt(x^2+34)

\int x^{3} x^{2} + 34 d x

limit as x approaches 4+of-3/(8-2x)

x \to 4 + lim (- \frac{3}{8 - 2 x})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^5-x^3+3)^4 ?
The derivative of f(x)=(x^5-x^3+3)^4 is 4(x^5-x^3+3)^3(5x^4-3x^2)
What is the first derivative of f(x)=(x^5-x^3+3)^4 ?
The first derivative of f(x)=(x^5-x^3+3)^4 is 4(x^5-x^3+3)^3(5x^4-3x^2)