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Popular >

derivative of f(x)=ax^4+(a-9)x^2-9

Solution

derivative of

f (x) = a x^{4} + (a - 9) x^{2} - 9

Solution

4 a x^{3} + 2 x (a - 9)

Solution steps

\frac{d}{d x} (a x^{4} + (a - 9) x^{2} - 9)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x^{4}) + \frac{d}{d x} ((a - 9) x^{2}) - \frac{d}{d x} (9)

\frac{d}{d x} (a x^{4}) = 4 a x^{3}

\frac{d}{d x} ((a - 9) x^{2}) = 2 x (a - 9)

\frac{d}{d x} (9) = 0

= 4 a x^{3} + 2 x (a - 9) - 0

Simplify

= 4 a x^{3} + 2 x (a - 9)

Popular Examples

sum from n=1 to infinity of (3n)/(n^2+4)

n = 1 \sum \infty \frac{3 n}{n ^{2} + 4}

integral of cos^2(kx)

\int cos^{2} (k x) d x

integral from 2 to 4 of x/(x^2+6x+13)

\int_{2}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

sum from n=0 to infinity of 1/(n^2)

n = 0 \sum \infty \frac{1}{n ^{2}}

(\partial)/(\partial x)(e^{6x+9y})

\frac{\partial}{\partial x} (e^{6 x + 9 y})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ax^4+(a-9)x^2-9 ?
The derivative of f(x)=ax^4+(a-9)x^2-9 is 4ax^3+2x(a-9)
What is the first derivative of f(x)=ax^4+(a-9)x^2-9 ?
The first derivative of f(x)=ax^4+(a-9)x^2-9 is 4ax^3+2x(a-9)