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Question
\frac{d}{dx}\left(\left(3-x^{2}\right)\left(x+4\right)\right)
Evaluate the derivative
3-3x^{2}-8x
Evaluate
\frac{d}{dx}\left(\left(3-x^{2}\right)\left(x+4\right)\right)
Simplify
\frac{d}{dx}\left(3x+12-x^{3}-4x^{2}\right)
\text{Use differentiation rule }\frac{d}{dx}\left(f\left(x\right)\pm g\left(x\right)\right)=\frac{d}{dx}\left(f\left(x\right)\right)\pm \frac{d}{dx}(g(x))
\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(12\right)-\frac{d}{dx}\left(x^{3}\right)-\frac{d}{dx}\left(4x^{2}\right)
Calculate
More Steps
Calculate
\frac{d}{dx}\left(3x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
3\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
3\times 1
Any expression multiplied by 1 remains the same
3
3+\frac{d}{dx}\left(12\right)-\frac{d}{dx}\left(x^{3}\right)-\frac{d}{dx}\left(4x^{2}\right)
\text{Use }\frac{d}{dx}(c)=0\text{ to find derivative}
3+0-\frac{d}{dx}\left(x^{3}\right)-\frac{d}{dx}\left(4x^{2}\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
3+0-3x^{2}-\frac{d}{dx}\left(4x^{2}\right)
Calculate
More Steps
Calculate
\frac{d}{dx}\left(4x^{2}\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
4\times \frac{d}{dx}\left(x^{2}\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
4\times 2x
Multiply the terms
8x
3+0-3x^{2}-8x
Solution
3-3x^{2}-8x
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