If fx-x-1x4-x3-2x3-4x2-2x-3- then - dydx-x-1 is

Let, derivative of x^4+x^3+2=L and derivative of x^3+4x^2+2x+3=K ⇒ f'(x)=(x+1)(L)(x^3+4x^2+2x+3)+(x+1)(x^4+x^3+2)(K)+(x^4+x^3+2)(x^3+4x^2+2x+3) ⇒ f'( 1)=(2 1+1) ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

If fx=x+1x4+x...

Question

If $f (x) = (x + 1) (x^{4} + x^{3} + 2) (x^{3} + 4 x^{2} + 2 x + 3),$ then ${\frac{d y}{d x} ∣ ∣ ∣}_{x = - 1}$ is

0

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Solution

The correct option is D $8$
Let, derivative of $x^{4} + x^{3} + 2 = L$
and derivative of $x^{3} + 4 x^{2} + 2 x + 3 = K$
$\Rightarrow f^{'} (x) = (x + 1) (L) (x^{3} + 4 x^{2} + 2 x + 3) + (x + 1) (x^{4} + x^{3} + 2) (K) + (x^{4} + x^{3} + 2) (x^{3} + 4 x^{2} + 2 x + 3)$
$\Rightarrow f^{'} (- 1) = (2 - 1 + 1) (3 - 1 - 2 + 4) = (2) (4) ∴ f^{'} (- 1) = 8$

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Composite Function

Standard XII Mathematics

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If f(x)=(x+1)(x4+x3+2)(x3+4x2+2x+3), then dydx∣∣∣x=−1 is

The correct option is D 8Let, derivative of x4+x3+2=L and derivative of x3+4x2+2x+3=K ⇒f′(x)=(x+1)(L)(x3+4x2+2x+3)+(x+1)(x4+x3+2)(K)+(x4+x3+2)(x3+4x2+2x+3) ⇒f′(−1)=(2−1+1)(3−1−2+4)=(2)(4)∴f′(−1)=8

If $f (x) = (x + 1) (x^{4} + x^{3} + 2) (x^{3} + 4 x^{2} + 2 x + 3),$ then ${\frac{d y}{d x} ∣ ∣ ∣}_{x = - 1}$ is