Find the derivative of tan &#x2061;<!-- ⁡ 1 4 &#x03C0;<!-- π 2 +

Daphne Fry

Daphne Fry

Answered question

2022-05-12

Find the derivative of tan ( 1 4 π ( 2 + x + 6 x 2 + 7 x 3 + 4 x 4 ) ).

Answer & Explanation

pomastitxz27r

pomastitxz27r

Beginner2022-05-13Added 16 answers

Combine π and 14.

ddx[π4(2+x+6x2+7x3+4x4)]

Since π4 is constant with respect to x, the derivative of π4(2+x+6x2+7x3+4x4) with respect to x is π4ddx[2+x+6x2+7x3+4x4].

π4ddx[2+x+6x2+7x3+4x4]

By the Sum Rule, the derivative of 2+x+6x2+7x3+4x4 with respect to x is ddx[2]+ddx[x]+ddx[6x2]+ddx[7x3]+ddx[4x4].

π4(ddx[2]+ddx[x]+ddx[6x2]+ddx[7x3]+ddx[4x4])

Since 2 is constant with respect to x, the derivative of 2 with respect to x is 0.

π4(0+ddx[x]+ddx[6x2]+ddx[7x3]+ddx[4x4])

Add 0 and ddx[x].

π4(ddx[x]+ddx[6x2]+ddx[7x3]+ddx[4x4])

Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=1.

π4(1+ddx[6x2]+ddx[7x3]+ddx[4x4])

Since 6 is constant with respect to x, the derivative of 6x2 with respect to x is 6ddx[x2].

π4(1+6ddx[x2]+ddx[7x3]+ddx[4x4])

Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=2.

π4(1+6(2x)+ddx[7x3]+ddx[4x4])

Multiply 2 by 6.

π4(1+12x+ddx[7x3]+ddx[4x4])

Since 7 is constant with respect to x, the derivative of 7x3 with respect to x is 7ddx[x3].

π4(1+12x+7ddx[x3]+ddx[4x4])

Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=3.

π4(1+12x+7(3x2)+ddx[4x4])

Multiply 3 by 7.

π4(1+12x+21x2+ddx[4x4])

Since 4 is constant with respect to x, the derivative of 4x4 with respect to x is 4ddx[x4].

π4(1+12x+21x2+4ddx[x4])

Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=4.

π4(1+12x+21x2+4(4x3))

Multiply 4 by 4.

π4(1+12x+21x2+16x3)

Simplify.

21πx24+3πx+4πx3+π4


 

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